ORIGINAL ARTICLE
Modeling the Effect of Herd Immunity and Contagiousness in Mitigating a Smallpox Outbreak Ellie Graeden, PhD, Russel Fielding, BSc, Kyle E. Steinhouse, BSc, Ilan N. Rubin, BA
The smallpox antiviral tecovirimat has recently been purchased by the U.S. Strategic National Stockpile. Given significant uncertainty regarding both the contagiousness of smallpox in a contemporary outbreak and the efficiency of a mass vaccination campaign, vaccine prophylaxis alone may be unable to control a smallpox outbreak following a bioterror attack. Here, we present the results of a compartmental epidemiological model that identifies conditions under which tecovirimat is required to curtail the epidemic by exploring how the interaction between contagiousness and prophylaxis coverage of the affected population affects the ability of the public health response to control a large-scale smallpox outbreak. Each parameter value in the model is based on published empirical data. We describe contagiousness parametrically using a novel method of distributing an assumed R-value over the disease course based on the relative rates of daily viral shedding from human and animal studies of cognate orthopoxvirus infections. Our results suggest
that vaccination prophylaxis is sufficient to control the outbreak when caused either by a minimally contagious virus or when a very high percentage of the population receives prophylaxis. As vaccination coverage of the affected population decreases below 70%, vaccine prophylaxis alone is progressively less capable of controlling outbreaks, even those caused by a less contagious virus (R0 less than 4). In these scenarios, tecovirimat treatment is required to control the outbreak (total number of cases under an order of magnitude more than the number of initial infections). The first study to determine the relative importance of smallpox prophylaxis and treatment under a range of highly uncertain epidemiological parameters, this work provides public health decision-makers with an evidence-based guide for responding to a large-scale smallpox outbreak. Key words: bioterrorism; disaster preparedness; probabilistic sensitivity analysis; formulary decision making; discrete event simulation. (Med Decis Making 2015;35:648–659)
INTRODUCTION
of vaccine and a newly developed antiviral against the agent. Because there has never been a large-scale terror attack with the variola virus or a contemporary outbreak, there are no data regarding the dynamics of a smallpox outbreak with a modern public health response system and the contemporary population. Therefore, there is significant uncertainty regarding how a public health response to an outbreak would unfold and how effective it would be. Here we present a model to test the relative value of the available medical countermeasures (the vaccine and an antiviral, both stockpiled in large quantity
Variola, the orthopox virus that causes smallpox, kills nearly 30% of those it infects and had a dramatic and continued effect on human history until its eradication in the 1970s. Although no longer a persistent public health threat, smallpox is of significant concern as a potential bioterror threat. To mitigate against that threat, the United States has stockpiled large amounts Received 11 October 2013 from Gryphon Scientific LLC, Takoma Park, Maryland. This work was completed as part of contract work supported by SIGA Technologies. SIGA Technologies is the producer of tecovirimat. These results were published independent of approval by the funding source, as stipulated by the contract. Revision accepted for publication 18 October 2014. Ó The Author(s) 2014 Reprints and permission: http://www.sagepub.com/journalsPermissions.nav DOI: 10.1177/0272989X14561681
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Supplementary material for this article is available on the Medical Decision Making Web site at http://mdm.sagepub.com/supplemental. Address correspondence to Ellie Graeden, PhD, Gryphon Scientific, 6930 Carroll Ave, Suite 810, Takoma Park, MD 20912, USA; telephone: (301) 270-0645; fax: (301) 270-0673; e-mail: ellie@gryphonscientific .com.
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by the US government) and a range of public health response characteristics that would alter the effectiveness of the public health response associated with their administration. The goal of this analysis is to compare the various public health response options to better inform the development of empirically derived emergency response plans. We have developed a simple decision support graphic designed to translate the outputs of this model for use by public health emergency planners. This analysis provides the first example of a data-driven decision support tool designed to translate the results of a comparative epidemiological modeling analysis into operations-focused information for public health emergency personnel. Uncertainty in Public Health Response Modeling An effective prophylaxis campaign requires that a significant percentage of the population receive the prophylaxis. However, coverage is a large source of uncertainty in modeling the efficacy of the public health response. There are no data available from recent outbreaks to assess the likely coverage of the smallpox vaccine (known to cause rare but severe adverse events) in the contemporary population. Similarly, there are no data available to suggest what percentage of the population would accept administration of an antiviral, such as tecovirimat, as prophylaxis. Even in high-risk, postevent scenarios in the past decade, the success of large-scale prophylaxis campaigns with either vaccines or antibiotics has been plagued by low coverage and compliance.1,2 Quantifying the contagiousness of variola in the contemporary population is also a major challenge plagued by significant uncertainty. This parameter is defined by the number of new infections transmitted by a smallpox patient over the course of his or her illness and reflects a combination of many factors. These factors are contingent on the biological characteristics of the virus as well as the immunological status, living conditions, and social interactions of the infected population. Therefore, smallpox contagiousness may be quite different in the contemporary population than in populations affected by the disease prior to its eradication. Epidemiological Modeling of Smallpox Under highly uncertain conditions for which there are little or no contemporary data available, epidemiological modeling is a powerful method to test public
health response plans against a wide range of possible scenarios. (While this model could not, therefore, be validated against event-specific data, the parameters were based on the best available scientific data for comparative studies, whether medical countermeasure efficacy studies or public health response studies for other diseases and types of response.) Computational modeling of smallpox has been used previously to compare various vaccination strategies and evaluate the relative importance of different aspects of the public health response (e.g., speed of detection, role of social structure, and value of social distancing).3–7 These studies have primarily focused on vaccination strategies or have analyzed specific aspects of the disease dynamics of naturally occurring outbreaks. For example, Kaplan et al.5 compared postevent mass vaccination with trace vaccination, and Meltzer et al.6 compared a quarantine strategy with a vaccination strategy. Additional models developed by Halloran et al.3 and Burke et al.4 used social networks of locations, including households, schools, and hospitals, to model the infection patterns and scale of outbreaks. Smallpox models such as those described by Eichner8 and by Riley and Ferguson9 analyzed contract tracing as a method of administering vaccine to contain a contemporary outbreak but with an initially infected population of 100 people or fewer. In only one prior study has the efficacy and effectiveness of tecovirimat been analyzed in the context of a smallpox outbreak. In this study, Finin et al.7 developed a model of the effectiveness of the public health response to a smallpox outbreak using vaccination with modified vaccinia Ankara (MVA) vaccine combined with tecovirimat postexposure prophylaxis or treatment. Finin et al. focused on the role of patient compliance on the overall efficacy of the public health response to a smallpox outbreak. While the study presents a careful analysis of the role of patient compliance on the efficacy of countermeasures in limiting an outbreak, this factor is not under the control of the public health community and cannot be used to support decision making in public health preparedness and response. Modeling for Public Health Decision Makers The model presented here is specifically designed to address the gaps in the previous smallpox models by assessing the value of tecovirimat in the prophylaxis and treatment of smallpox compared with a public health response based solely on vaccination. Using our smallpox model, we have explored the effect of uncertainty regarding contagiousness and
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Figure 1 Transition of the population through the incubation period when modeled as 12 single-day periods. Modeling the incubation period in 12 steps yields a distribution of cases (solid line) most similar to that of the human disease course (vertical bars). The distribution of cases as a function of the number of days spent in the incubation period is shown as modeled in a single-step (dotted line), two-step (dashed line), or 12-step (solid line) incubation period compared with the distribution of empirical data from reports of the human disease course.10,11
prophylaxis coverage on the relative value of vaccination and tecovirimat as prophylaxis and treatment administered in response to a large-scale outbreak. We present an in-depth analysis of the parametric effect of contagiousness and prophylaxis coverage on a smallpox outbreak and provide an evidencebased decision support tool that can be used to help inform decisions in public health preparedness and response, a critical downstream application of this type of analysis. METHODS Model Framework The model we developed is an expanded SEIR (susceptible-exposed-infectious-recovered) compartmental system of ordinary differential equations describing a large-scale smallpox outbreak in New York City (see Figure 2). To more accurately model the severity of the disease and efficacy of medical countermeasures, the population is divided into subpopulations based on immune status (normal, prevaccinated, and immunocompromised) and disease type (ordinary, modified, and hemorrhagic). The results of the model establish the relative effectiveness of various combinations of medical
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countermeasures administered as prophylaxis or treatment during a smallpox outbreak, as well as the public health responses necessary to disseminate those countermeasures to the affected population in reducing morbidity and mortality. The parameters were developed from empirical evidence in the published literature. The values associated with the population-level transmission of disease and the public health response were established based on a literature review and analysis of the data from previous smallpox outbreaks supplemented with data from outbreaks of diseases for which there have been more recent outbreaks, such as influenza and meningitis. Vaccine efficacy was based on the extensive data collected during the eradication campaign in the middle of the 20th century. The efficacy of tecovirimat was evaluated using data from disease in animal models infected with orthopoxviruses that most closely recapitulate the human disease course. Each parameter is incorporated in the model as a constant or variable in the differential rate equations that define movement between each stage of the disease course. After the initial population is infected, subsequent infection of the susceptible population is determined by the force of infection, defined as the rate susceptible individuals become infected. Contagiousness is approximated as the R0 distributed over the length of the contagious period based on the viral shedding rate for each disease stage. Once infected, the incubating population either continues onto each subsequent day of the incubation period or is administered prophylaxis. The population receiving prophylaxis is limited by the rate at which vaccinations can be administered during a public health response. The incubation period is divided into 12 single-day time steps through which the population moves sequentially. The population experiencing the ordinary or modified disease type then progresses into the prodromal stage of the disease. The fraction of the population experiencing hemorrhagic disease moves into a parallel path for the symptomatic stage in which they can receive treatment if not contraindicated. In the hemorrhagic form of disease, fever and rash occur simultaneously and are modeled accordingly. Those receiving treatment (all those not contraindicated) move into parallel paths based on their disease type with reduced levels of contagiousness. The reduction in contagiousness is based on the percent reduction in viral shedding by treatment with tecovirimat. After completing the disease course, each subpopulation moves into either the dead or recovered categories based on case fatality rates for
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Figure 2 Model framework shows the smallpox disease course and interactions between contagious and susceptible populations. Model framework outlines the disease course and available medical countermeasures. The solid lines indicate the flow of the population through the smallpox disease course. Patients with ordinary and modified smallpox flow through the fever and overtly symptomatic or rash stages. Hemorrhagic patients flow through a single symptomatic, contagious period (‘‘Hemorrhagic’’). The paths describing prophylaxis or treatment are opened at the onset of the public health response. All those receiving effective prophylaxis become protected. All those eligible for treatment move into a late disease stage corresponding to rash and then to dead or recovered based on treatment efficacy. Dotted lines represent the interaction of contagious populations with the susceptible populations, which determines the rate of new infections and corresponding flow into the incubation period.
each combination of disease type and subset of the population. The paths for prophylaxis and treatment become available only once the outbreak has been recognized and the medical countermeasures (MCMs) have been made available to the population. See the technical appendix in Additional File 2 for a detailed description of the equations and modeling methods. Parameters Disease Course We modeled the 3 primary clinical forms of smallpox: ordinary, hemorrhagic, and modified. In ordinary smallpox, the asymptomatic incubation stage lasts an average of 12 days and is followed by a 3day prodromal stage marked by fever.12–17 The overtly symptomatic (rash) stage is characterized first by rash and then by the eruption of pox or pustules. This stage typically lasts 8 to 11 days, ending with either death or recovery.12,13 Hemorrhagic smallpox has a case fatality rate (CFR) of 95% and primarily affects pregnant women and infants18; we assume the entire immunocompromised population (as defined in Appendix 1) would be similarly affected. Ordinary smallpox has a 30% CFR and affects the majority of the population.12,13 The modified form has a CFR near zero and primarily affects those with
partial resistance from previous vaccination. The distribution of the population between these subpopulations and their relative likelihood of contracting smallpox is described in detail in the technical appendix in Additional File 1. The transition of the population through the incubation period is modeled not as one 12-day stage but as 12 stages, each lasting one day. This division of the incubation period corrects the overestimation of the rate of transition for the majority of the population that occurs with a single, exponentially distributed incubation stage (see Figure 1).19 Medical Countermeasure Efficacy None of the MCMs against smallpox currently stockpiled by the US federal government, including ACAM2000 and tecovirimat, have been tested against the disease in humans. The efficacy of the vaccine, ACAM2000, in preventing infection is based on earlier vaccines.12,20 The MVA vaccine, intended for use in populations contraindicated for ACAM2000, requires 2 doses at a month interval and does not provide maximum protection until 6 weeks after the first dose, so while the vaccine may have some benefit, it would likely have limited utility during a postevent public health response and is not included here.21 ACAM2000 is modeled as 98% effective at preventing the onset of symptoms if administered prior to
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infection and as 54% effective at preventing the onset of symptoms if administered in the first 8 days of the incubation period.12,13,22,23 The efficacy of tecovirimat both as prophylaxis in preventing the onset of symptoms or as treatment in preventing fatalities is extrapolated from animal models of lethal orthopoxvirus infection.24–27 The efficacy of the antiviral as prophylaxis was tested in nonhuman primates infected intravenously with monkeypox (the animal model most similar to the ordinary smallpox disease course in humans). The antiviral was administered immediately after intravenous injection of the virus, which marked the onset of infection, and on days 1, 2, and 3 postinfection.24 In all cases, prophylactic treatment (days 1 and 2 postinfection) prevented both disease and death in 100% of treated animals (6/6 monkeys), while 0% (0/3) mock-treated monkeys survived. Because only 6 animals were used in this experiment, this assay could not distinguish between a countermeasure that was only 89.1% effective (89.1% is the smallest probability of individual survival resulting in an expected survival of all 6 monkeys slightly more than 50% of the time) v. one that is 100% effective. To be conservative, we therefore assumed that the countermeasure has the least possible efficacy given the number of animals in this experiment. Based on data from a study that established tecovirimat efficacy for mice with varying levels of partial immune deficiency, treatment prevented both disease and death in 100% of animals when administered on the same day as infection (30/30 mice).26 On the basis of these data, we assumed the same level of tecovirimat prophylaxis efficacy (89.1%) for the immunocompromised population as for the normal and prevaccinated subsets of the population. Because the onset of the prodromal period is defined by the onset of symptoms (fever), efficacy during prodrome is defined by prevention of mortality, not morbidity. In nonhuman primates infected with monkeypox, fever is first detected 3 days postinfection.24 Therefore, we included in our analysis only the data that describe the efficacy of tecovirimat administered on the third day postinfection to monkeys infected intravenously with monkeypox. Treatment on day 3 postinfection was 100% effective in preventing mortality (15/15 animals tested in 2 studies with 0/6 mock-treated animals surviving).24,25 Therefore, we assumed that antiviral treatment during prodrome is 95.5% effective in preventing mortality when adjusted to account for the small sample size (reduced from 100% to account for the
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fact that only 15 animals were tested). Similarly, the efficacy was determined by the most conservative estimate calculated on the basis of the number of animals tested. In immunocompromised mice, the survival rate dropped to 80% when treatment was postponed until 3 days after infection.26 Therefore, we assumed that the efficacy of tecovirimat treatment during prodrome of the immunocompromised population is 80%. The ‘‘rash stage’’ is characterized by the onset of lesions, which occurs 4 days postinfection in monkeys infected with monkeypox intravenously.24 Antiviral treatment starting 4 days postinfection has varying results depending on dosage.27 We assume that the drug will be administered at ~6 mg/kg (400 mg/70 kg adult),25 a dosage at which the drug was 89% effective when administered 4 days postinfection. Therefore, we assume that antiviral treatment on the first day of the rash stage is 89% effective. Tecovirimat can be administered either orally by pill or by intravenous injection (IV); the oral form has completed a phase II clinical study published with the Food and Drug Administration.27 Based on data suggesting that the blood level concentrations are comparable between the 2 routes of administration, we assumed no difference in the efficacy or rates of adverse events between the 2 methods.28 We assume no contraindications for vaccination based on the Centers for Disease Control and Prevention (CDC) response plans for postevent vaccination.29 There are no known contraindications for tecovirimat; however, we excluded people unable to swallow pills from the population eligible for oral administration of the antiviral.30–32 Public Health Response We model the public health response to a smallpox outbreak in New York City. The model outbreak is initiated when the first person becomes infected with smallpox. Importantly, the goal of this work is to model the current, planned public health response to a smallpox outbreak (vaccination) to a response bolstered by the use of tecovirimat. While ring vaccination may be considered at the outset of an outbreak, a rapid accumulation of new patients seeking care who have no obvious connection to each other would suggest that a large-scale release of virus had occurred. With a very large number of infections likely, and without additional information about the source of the infections, such a large influx of unrelated patients would quickly overwhelm the ability to trace all the contacts for these patients in a short period of time. Therefore, ring
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vaccination is an unlikely scenario in a contemporary, large-scale outbreak. We modeled a postevent region-specific mass vaccination campaign, as recommended by the CDC for large-scale outbreaks and shown to be most effective in earlier modeling efforts.5,33 On the basis of these references, we assume that vaccinations and oral antiviral will be administered to all those eligible in the affected region from points of dispensing/vaccination managed by the federal government, deployed once the outbreak has been recognized.5,33 The range of possible rates of administering vaccinations or coadministering vaccinations and oral antiviral prophylaxis is based on data from the City Readiness Initiative, simulated smallpox vaccination clinics, and actual public health responses to meningitis and influenza outbreaks.1,34–36 A public health response is initiated only once the outbreak is recognized and the necessary MCMs have been transported to the site of the outbreak. In the 2003 monkeypox outbreak in the United States, response was not initiated until 20 cases were seen in area hospitals.37 In our model, we assume a somewhat more optimistic scenario in which the outbreak will be recognized and a large-scale public health response mounted once 10 cases reach the fulminant stage (concomitant with presentation of pox). A sensitivity analysis of the case delay, ranging from 1 to 50 fulminant cases, was completed and is presented in Appendix 3. Defining this delay in cases (the ‘‘case delay’’) instead of days automatically corrects for a reduction in the recognition delay during larger outbreaks. The recognition delay is defined by the amount of time between when the first symptomatic smallpox patient arrives for care and when he or she is first correctly diagnosed (we assume that smallpoxspecific treatment will be administered only once the patient has been diagnosed with the disease). The case delay will be shorter for larger outbreaks, if calculated based on the number of symptomatic patients seeking medical care. The delay in mounting an effective and disease-specific response is modeled by the ‘‘response delay,’’ defined by the time estimated by the CDC for distribution of supplies from the Strategic National Stockpile.38 We assume a 2day delay before the necessary supplies are delivered from the Strategic National Stockpile and the mass prophylaxis campaign is initiated. A sensitivity analysis was completed and included in Appendix 3. Complete prophylaxis (100% coverage and compliance) of the population within 25 days was assumed as the baseline for mitigation scenarios, but the full
extent of coverage achieved is explored in this analysis. As our model attempts to quantify the theoretical maximum effectiveness of medical countermeasures, we also assume that medical countermeasures will be unlimited in supply. Any limitation under mass prophylaxis would affect the outcome similarly to reductions in prophylaxis coverage rates in the population. Contagiousness The contagiousness of a disease is often quantified as the basic reproductive number, R0, defined as the expected number of secondary infections caused by a single case introduced into a completely susceptible population. Previous studies falsely assumed a large part of the R0 of smallpox was due to infectiousness during the prodromal stage of the disease rather than during the symptomatic stage.39 To more accurately represent contagiousness, we approximated contagiousness as a function of previously published R0 values for smallpox but distributed over the disease course based on viral shedding rates extrapolated from a combination of animal and human studies.40,41 The amount of virus shed by an infected patient is an indicator of his or her contagiousness, and viral shedding, unlike many of the factors affecting contagiousness, can be quantified over the smallpox disease course. Viral shedding rates, defined by the amount of virus released into the environment by an infected patient at any given point in his or her illness, vary significantly on each day of disease.40 Because data are limited for human shedding rates, macaque data were used to help determine the relative viral shedding rates for each day over the course of the disease (Appendix 1).40,41 When normalized for the differing lengths of the disease course, viral shedding peaks on the last day of fever and first day of pox and is no longer detectable by day 13 of symptomatic illness. In the absence of data describing viral shedding during prodrome in humans, we adjusted the mean viral shedding rate based on the relative length of the macaque and human prodromal periods. Previous modeling efforts and analyses of smallpox outbreaks suggest a wide range for the possible R0 of smallpox. The R0 has most often been estimated to be between 3.5 and 6 in contemporary populations; we assume a baseline R0 of 5 but consider a range from 1.5 to 18, with the upper limit defined by the established R0 of measles, considered the most contagious of human diseases.3,5,42–46 Tecovirimat is an egress inhibitor; treatment with the antiviral reduces viral shedding by 22-fold in animals infected with orthopoxvirus.47 Based on these
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animal data, our model thus assumed a 22-fold reduction in contagiousness in patients receiving antiviral treatment. Based on studies of contact rates in contemporary populations both under normal and epidemic conditions, contact rates and, correspondingly, contagiousness, will drop by 52.1% (from 11.5 contacts per day per person under normal conditions to 6 contacts per day per person) after a smallpox outbreak is recognized and the public health response initiated due to social distancing measures.48–51
are accurately diagnosed), treatment is administered to patients in the rash stage. Treatment significantly reduces viral shedding and therefore contagiousness; there is a corresponding reduction in caseload with the addition of tecovirimat treatment compared with vaccination-only scenarios across a range of public health response assumptions. As shown in Figure 3D, administering antiviral treatment also significantly reduces cumulative fatalities compared with vaccination-only scenarios. This reduction in mortality is largest at the height of the outbreak, around a month after the initial population is infected.
RESULTS Effect of Prophylaxis Coverage on Caseload MCM Efficacy in an Outbreak Figure 3 compares the effect of no mitigation, vaccination alone, or vaccination prophylaxis and tecovirimat treatment on morbidity and mortality for each day of a smallpox outbreak with 1000 people initially infected. Figure 3A,B shows an unmitigated disease scenario and both mitigation scenarios, and Figure 3C,D shows only the mitigated scenarios. Caseload is defined by the number of people reaching prodrome, which marks the onset of symptoms and the beginning of the contagious stage of disease. The results shown here are based on scenarios assuming 100% prophylaxis coverage of the population with an R0 of 5 (with contagiousness distributed proportionally to viral shedding rates over the contagious period) and are consistent across scenarios based on a range of public health assumptions (data not shown). The effect of these assumptions is considered in detail in the remainder of this study. As shown in Figure 3A,C, any mitigation, both vaccination alone as well as vaccination and tecovirimat treatment, greatly reduces the effects of the epidemic. Vaccination alone reduced the total morbidity of the epidemic from 13.7 million cases to 2861, while treatment in addition to vaccination further reduced morbidity to 1961 cases. Similarly, vaccination alone reduced the total mortality from 4.9 million deaths to 1160, and vaccination plus treatment further reduced the death toll to 126. For mitigation scenarios, shown in Figure 3B, the number of new cases per day increases over the first 2 weeks as those initially infected with smallpox become symptomatic, at which point they become contagious and begin infecting others. The number of new cases per day drops before the second wave of patients moves from incubation into prodrome. Once the public health response is initiated (after 10 cases begin exhibiting the hallmark symptom, pox,
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The extent to which a mass vaccination campaign can reach all susceptible people is unknown. To address this uncertainty, we calculated the effect of prophylaxis coverage rates on the ability of vaccination alone and vaccination prophylaxis with tecovirimat treatment to control an outbreak. As shown in Figure 4, the percentage of the population receiving effective prophylaxis has a significant, nonlinear effect on the total caseload during an outbreak with 1000 initial infections. The total caseload increases dramatically in vaccination-only scenarios when less than 80% of the population receives prophylaxis. When 50% of the population receives prophylaxis, the outbreak is limited in size only by the total number of people in the initial susceptible population. By contrast, vaccination prophylaxis and tecovirimat treatment successfully control the outbreak unless prophylaxis coverage drops to 20% or less. (An outbreak is considered controlled when the secondary cases outnumber primary cases by less than 10 to 1.) Tecovirimat is effective as prophylaxis throughout the incubation stage (in comparison to vaccination, which is effective only early in the incubation period), and coadministering the antiviral with vaccination as prophylaxis also reduces total morbidity and mortality but to a lesser extent (data not shown). The results here include only vaccination; these results are not significantly affected when tecovirimat is additionally administered as prophylaxis (data not shown). Effect of Contagiousness on Caseload The contagiousness of smallpox in a modern outbreak is highly uncertain. To address this uncertainty, we compared the effect of a wide range of contagiousness on the size of outbreaks in which
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Figure 3 Tecovirimat treatment significantly reduces both morbidity and mortality. Results shown from model scenarios with 1000 initial infections, an R0 of 5, and 100% prophylaxis. Scenarios considered include those in which vaccine alone is administered as prophylaxis (solid lines), vaccine is administered as prophylaxis and tecovirimat as treatment (dashed lines), and no mitigation (dotted lines). (A) The number of new cases reaching the prodromal stage (symptomatic and contagious) is shown for the 2 mitigation and the no-mitigation scenarios. (B) The number of new cases reaching the prodromal stage (symptomatic and contagious) is shown for the 2 mitigation scenarios only. (C) The number of fatalities is shown for the 2 mitigation and the no-mitigation scenarios. (D) The number of fatalities is shown for the 2 mitigation scenarios only.
Figure 4 Prophylaxis coverage has a large, nonlinear effect on caseload. The total number of cases from outbreaks with 1000 initial infections is shown on a log scale for scenarios in which the percentage of the population receiving vaccine prophylaxis ranges from 100% to 0%. Caseloads for outbreaks in which vaccine prophylaxis alone is administered are shown with a solid line; caseloads for outbreaks with vaccine prophylaxis and tecovirimat treatment administered are shown with a dashed line; caseloads for outbreaks with no mitigation are shown with a dotted line. The total population is marked with a double solid line.
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100,000,000
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Ro Figure 5 Contagiousness has a large, nonlinear effect on caseload. The total number of cases in outbreaks with 1000 initial infections is shown on a log scale based on scenarios with contagiousness parameters based on R-values ranging from 1.5 to 18. Caseloads for outbreaks in which vaccine prophylaxis alone is administered are shown with a solid line; caseloads for outbreaks with vaccine prophylaxis and tecovirimat treatment administered are shown with a dashed line; caseloads for outbreaks with no mitigation are shown with a dotted line. The total population is marked with a double solid line.
vaccination alone was administered or both vaccine prophylaxis and tecovirimat treatment were administered. As shown in Figure 5, the caseload of an outbreak is also highly sensitive to the relative contagiousness of the virus, modeled by distributing R0 proportionally over the disease course (see Methods). In postevent vaccination scenarios assuming that 50% of the population receives effective prophylaxis but no treatment is available, the outbreak infects at least 10-fold more victims than were initially infected when the R0 is just over 3 or higher. In scenarios with antiviral treatment administered in conjunction with vaccine prophylaxis, the outbreak is controlled (fewer than 10,000 total cases) as long as the R0 is 7 or less. The effect of contagiousness on the caseload in these outbreaks is consistent whether vaccination alone or vaccination and tecovirimat are administered as prophylaxis (data not shown). Outbreak Control Considering Both Prophylaxis Coverage and Contagiousness As shown in Figure 6, we determined the interaction between disease contagiousness and prophylaxis coverage to identify conditions under which vaccination alone is sufficient to control an outbreak
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and when tecovirimat treatment is required. The heat map shows the percentage of the population receiving prophylaxis on one axis and the relative contagiousness of the virus on the other. The map highlights conditions under which the outbreak is controlled by prophylaxis alone, is contained by prophylaxis plus treatment, or is uncontained (as described above, an uncontained outbreak is one in which secondary cases outnumber primary cases by 10 to 1). At high levels of prophylaxis coverage and low contagiousness, vaccination alone is sufficient to control the modeled outbreak. However, there are a large number of plausible scenarios under which tecovirimat treatment is necessary to control the outbreak. Outbreaks of a highly contagious virus in which less than 70% of the population receives prophylaxis are not controlled even when both vaccine prophylaxis and antiviral treatment are administered. Including tecovirimat as prophylaxis does not affect these breakpoints (data not shown). CONCLUSIONS With the addition of tecovirimat to the Strategic National Stockpile, the United States has, for the first
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Figure 6 Heat map showing the relative importance of prophylaxis coverage for outbreaks with virus of varying levels of contagiousness. Heat map is coded by whether the smallpox outbreak is uncontrolled, where an uncontrolled outbreak is one in which secondary cases outnumber primary cases by 10 to 1 (e.g., more than 10,000 for outbreaks with 1000 people initially infected). Outbreaks in which vaccine prophylaxis alone controls the outbreak are shown in light gray; outbreaks in which adding tecovirimat treatment is sufficient to control the outbreak are shown in dark gray; outbreaks in black are not controlled even with both vaccine prophylaxis and treatment administered.
time, an effective treatment for smallpox. The effect of uncertainty regarding prophylaxis coverage rates or viral contagiousness on the value of this antiviral in mitigating an outbreak has not previously been determined. The analysis presented here addresses the efficacy of tecovirimat in the treatment of smallpox when coadministered with the vaccine considering these sources of uncertainty. The results presented here suggest that both prophylaxis coverage of the population and contagiousness have a large, nonlinear effect on the size of a smallpox outbreak. With an R0 of 5 and no treatment, prophylaxis coverage of the population must be 80% to control the outbreak, whereas when tecovirimat treatment is included, the outbreak is controlled with only 30% prophylaxis coverage. Prophylaxis coverage of previous vaccination campaigns, even for highly contagious, highly deadly diseases in populations with few contraindications, has been as low as 50% (such as during the meningitis outbreak on the Michigan State University campus in the early 2000s).1 Vaccination compliance rates in a mock smallpox-vaccination exercise in San Francisco were also near 50%.35 Taken together, these data suggest that the proportion of the population receiving prophylaxis could well be less than 80%,
and tecovirimat treatment would be required to control the outbreak. As described here, our results suggest that, assuming 50% prophylaxis coverage, vaccination alone can control the outbreak only if the R0 is less than 4. If the R0 is greater than 4, tecovirimat treatment is required to control the outbreak. Neither measure is sufficient to control outbreaks in which the R0 is greater than 7. A rigorous analysis of historical outbreak reports from Europe over the past few centuries calculated the likely R0 of smallpox as between 3.5 and 6, and these authors suggest that these values may be an underestimate of the contagiousness of smallpox in a contemporary outbreak due to increases in population density and a lack of herd immunity.42 Under such conditions, tecovirimat treatment administration in conjunction with vaccine prophylaxis is required to control the outbreak. The results of this study suggest that including an effective treatment in the public health response to a large-scale smallpox outbreak significantly expands the range of outbreak scenarios that can be controlled with the current medical countermeasures available. There is great uncertainty surrounding the epidemiology of smallpox and the ability of public health to vaccinate all susceptible people in an outbreak.
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These data provide the evidence basis for effective decision making when developing emergency public health plans for a contemporary smallpox outbreak.
the incubation period distribution. Int J Hyg Environ Health. 2009;212(1):97–104. 18. Rao AR, Prahlad I, Swaminathan M, Lakshmi A. Pregnancy and smallpox. J Indian Med Assoc. 1963;40:353–63. 19. Lloyd AL. Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics. Theor Popul Biol. 2001;60(1):59–71.
ACKNOWLEDGMENTS We thank Rocco Casagrande and Mark Kazmierczak for their contributions to and review of both the model and manuscript and Anna Kushnir for her review and editing of the manuscript.
20. Nalca A, Zumbrun EE. ACAM2000: the new smallpox vaccine for United States Strategic National Stockpile. Drug Design Dev Ther. 2010;4:71–9. 21. Henderson DA. Smallpox virus destruction and the implications of a new vaccine. Biosecur Bioterror. 2011;9(2):163–8.
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22. Massoudi MS, Barker L, Schwartz B. Effectiveness of postexposure vaccination for the prevention of smallpox: results of a delphi analysis. J Infect Dis. 2003;188(7):973–6.
1. Paneth N, Kort EJ, Gibbons C, et al. Predictors of vaccination rates during a mass meningococcal vaccination program on a college campus. J Am Coll Health. 2000;49(1):7–11.
23. Heiner G, Fatima N, McCrumb F. A study of intrafamilial transmission of smallpox. Geneva, Switzerland: World Health Organization; 1971.
2. Borio LL, Gronvall GK. Anthrax countermeasures: current status and future needs. Biosecur Bioterror. 2005;3(2):102–12. 3. Halloran ME, Longini IM Jr, Nizam A, Yang Y. Containing bioterrorist smallpox. Science. 2002;298(5597):1428–32.
24. Huggins J, Goff A, Hensley L, et al. Nonhuman primates are protected from smallpox virus or monkeypox virus challenges by the antiviral drug ST-246. Antimicrob Agents Chemother. 2009; 53(6):2620–5.
4. Burke DS, Epstein JM, Cummings DA, et al. Individual-based computational modeling of smallpox epidemic control strategies. Acad Emerg Med. 2006;13(11):1142–9.
25. Jordan R, Goff A, Frimm A, et al. ST-246 antiviral efficacy in a nonhuman primate monkeypox model: determination of the minimal effective dose and human dose justification. Antimicrob Agents Chemother. 2009;53(5):1817–22.
5. Kaplan EH, Craft DL, Wein LM. Emergency response to a smallpox attack: the case for mass vaccination. Proc Natl Acad Sci U S A. 2002;99(16):10935–40. 6. Meltzer MI, Damon I, LeDuc JW, Millar JD. Modeling potential responses to smallpox as a bioterrorist weapon. Emerg Infect Dis. 2001;7(6):959–69. 7. Finin P, Kosaraju A, Rose E, Rubin H. The role of vaccination, antiorthopoxvirus drug, and social cooperativity in a mathematical model of smallpox control. Biosecur Bioterror. 2013;11(1):59–72. 8. Eichner M. Case isolation and contact tracing can prevent the spread of smallpox. Am J Epidemiol. 2003;158(2):118–28. 9. Riley S, Ferguson NM. Smallpox transmission and control: spatial dynamics in Great Britain. Proc Natl Acad Sci U S A. 2006; 103(33):12637–42. 10. Mack TM. Smallpox in Europe, 1950–1971. J Infect Dis. 1972; 125(2):161–9.
26. Grosenbach DW, Berhanu A, King DS, et al. Efficacy of ST-246 versus lethal poxvirus challenge in immunodeficient mice. Proc Natl Acad Sci U S A. 2010;107(2):838–43. 27. SIGA Technologies. Briefing book: background package for FDA advisory committee meeting on December 14–15, 2011. Available from: http://www.fda.gov/downloads/AdvisoryCom mittees/CommitteesMeetingMaterials/Drugs/AntiviralDrugsAdvis oryCommittee/UCM283286.pdf 28. Chen Y, Amantana A, Tyavanagimatt SR, et al. Comparison of the safety and pharmacokinetics of ST-246(R) after i.v. infusion or oral administration in mice, rabbits and monkeys. PLoS ONE. 2011;6(8):e23237. 29. Centers for Disease Control and Prevention. Smallpox: response 2009. Available from: http://emergency.cdc.gov/agent/ smallpox/response/.
11. Downie AW. Incubation period of smallpox. Geneva, Switzerland: World Health Organization; 1972.
30. Lindgren S, Janzon L. Prevalence of swallowing complaints and clinical findings among 50-79-year-old men and women in an urban population. Dysphagia. 1991;6(4):187–92.
12. Fenner F HD, Arita I, Jezek J, Ladnyi ID. Smallpox and its eradication. Geneva, Switzerland: World Health Organization; 1988.
31. US Census Bureau. Age and sex composition: 2010. Available from: http://www.census.gov/prod/cen2010/briefs/c2010br-03.pdf.
13. Rao AR. Smallpox. Bombay, India: Kothari Book Depot; 1972.
32. Chinsangaram J, Honeychurch KM, Tyavanagimatt SR, et al. Safety and pharmacokinetics of the anti-orthopoxvirus compound ST-246 following a single daily oral dose for 14 days in human volunteers. Antimicrob Agents Chemother. 2012;56(9):4900–5.
14. Mack TM, Thomas DB, Khan MM. Variola major in West Pakistan. J Infect Dis. 1970;122(6):479–88. 15. Wehrle PF, Posch J, Richter KH, Henderson DA. An airborne outbreak of smallpox in a German hospital and its significance with respect to other recent outbreaks in Europe. Bull World Health Organ. 1970;43(5):669–79.
33. Centers for Disease Control and Prevention (CDC). Smallpox response plan and guidelines (version 3.0). Atlanta, GA: CDC; 2002.
16. Lyons J, Dixon CW. Smallpox in the industrial Pennines. Med Officer. 1953;1953(90):293–300, 7–10.
34. Rinchiuso-Hasselmann A, Starr DT, McKay RL, Medina E, Raphael M. Public compliance with mass prophylaxis guidance. Biosecur Bioterror. 2010;8(3):255–63.
17. Nishiura H. Determination of the appropriate quarantine period following smallpox exposure: an objective approach using
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Department of Health. 2003. Available from: http://www.cdc.gov/ flu/pdf/professionals/vaccination-ventures-explanation-and-outcom es-of-mass-smallpox-vaccination-exercises.pdf. 36. Agocs M, Fitzgerald S, Alles S, et al. Field testing a head-ofhousehold method to dispense antibiotics. Biosecur Bioterror. 2007;5(3):255–67. 37. Sejvar JJ, Chowdary Y, Schomogyi M, et al. Human monkeypox infection: a family cluster in the midwestern United States. J Infect Dis. 2004;190(10):1833–40. 38. Centers for Disease Control, Office of Public Health Preparedness and Response. Strategic National Stockpile (SNS) 2011. Available from: www.cdc.gov/phpr/stockpile/stockpile.htm. 39. Ferguson NM, Keeling MJ, Edmunds WJ, et al. Planning for smallpox outbreaks. Nature. 2003;425(6959):681–5. 40. Sarkar JK, Mitra AC, Mukherjee MK, De SK, Mazumdar DG. Virus excretion in smallpox, 1: excretion in the throat, urine, and conjunctiva of patients. Bull World Health Organ. 1973;48(5): 517–22. 41. Stittelaar KJ, van Amerongen G, Kondova I, et al. Modified vaccinia virus Ankara protects macaques against respiratory challenge with monkeypox virus. J Virol. 2005;79(12):7845–51. 42. Gani R, Leach S. Transmission potential of smallpox in contemporary populations. Nature. 2001;414(6865):748–51. 43. Meltzer MI, Damon I, LeDuc JW, Millar JD. Modeling potential responses to smallpox as a bioterrorist weapon. Emerg Infect Dis. 2001;7(6):959–69.
44. Aldis GK, Roberts MG. An integral equation model for the control of a smallpox outbreak. Math Biosci. 2005;195(1):1–22. 45. Del Valle S, Hethcote H, Hyman JM, Castillo-Chavez C. Effects of behavioral changes in a smallpox attack model. Math Biosci. 2005;195(2):228–51. 46. Anderson RM, May RM. Infectious diseases of humans: dynamics and control. Oxford, UK: Oxford University Press; 1991. 47. Berhanu A, King DS, Mosier S, et al. ST-246 inhibits in vivo poxvirus dissemination, virus shedding, and systemic disease manifestation. Antimicrob Agents Chemother. 2009;53(12):4999–5009. 48. Destefano F, Haber M, Currivan D, et al. Factors associated with social contacts in four communities during the 2007-2008 influenza season. Epidemiol Infect. 2010;10:1–10. 49. Mossong J, Hens N, Jit M, et al. Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Med. 2008; 5(3):e74. 50. Rao AR, Jacob ES, Kamalakshi S, Appaswamy S, Bradbury. Epidemiological studies in smallpox: a study of intrafamilial transmission in a series of 254 infected families. Indian J Med Res. 1968; 56(12):1827–54. 51. Xinghuo P, Yang P, Shuang L, et al. Pandemic (H1N1) 2009 among quarantined close contacts, Beijing, People’s Republic of China. Emerg Infect Dis. 2011;17(10).
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Modeling the Effect of Herd Immunity and Contagiousness in Mitigating a Smallpox Outbreak Ellie Graeden, PhD, Russel Fielding, BSc, Kyle E. Steinhouse, BSc, Ilan N. Rubin, BA
The smallpox antiviral tecovirimat has recently been purchased by the U.S. Strategic National Stockpile. Given significant uncertainty regarding both the contagiousness of smallpox in a contemporary outbreak and the efficiency of a mass vaccination campaign, vaccine prophylaxis alone may be unable to control a smallpox outbreak following a bioterror attack. Here, we present the results of a compartmental epidemiological model that identifies conditions under which tecovirimat is required to curtail the epidemic by exploring how the interaction between contagiousness and prophylaxis coverage of the affected population affects the ability of the public health response to control a large-scale smallpox outbreak. Each parameter value in the model is based on published empirical data. We describe contagiousness parametrically using a novel method of distributing an assumed R-value over the disease course based on the relative rates of daily viral shedding from human and animal studies of cognate orthopoxvirus infections. Our results suggest
that vaccination prophylaxis is sufficient to control the outbreak when caused either by a minimally contagious virus or when a very high percentage of the population receives prophylaxis. As vaccination coverage of the affected population decreases below 70%, vaccine prophylaxis alone is progressively less capable of controlling outbreaks, even those caused by a less contagious virus (R0 less than 4). In these scenarios, tecovirimat treatment is required to control the outbreak (total number of cases under an order of magnitude more than the number of initial infections). The first study to determine the relative importance of smallpox prophylaxis and treatment under a range of highly uncertain epidemiological parameters, this work provides public health decision-makers with an evidence-based guide for responding to a large-scale smallpox outbreak. Key words: bioterrorism; disaster preparedness; probabilistic sensitivity analysis; formulary decision making; discrete event simulation. (Med Decis Making 2015;35:648–659)
INTRODUCTION
of vaccine and a newly developed antiviral against the agent. Because there has never been a large-scale terror attack with the variola virus or a contemporary outbreak, there are no data regarding the dynamics of a smallpox outbreak with a modern public health response system and the contemporary population. Therefore, there is significant uncertainty regarding how a public health response to an outbreak would unfold and how effective it would be. Here we present a model to test the relative value of the available medical countermeasures (the vaccine and an antiviral, both stockpiled in large quantity
Variola, the orthopox virus that causes smallpox, kills nearly 30% of those it infects and had a dramatic and continued effect on human history until its eradication in the 1970s. Although no longer a persistent public health threat, smallpox is of significant concern as a potential bioterror threat. To mitigate against that threat, the United States has stockpiled large amounts Received 11 October 2013 from Gryphon Scientific LLC, Takoma Park, Maryland. This work was completed as part of contract work supported by SIGA Technologies. SIGA Technologies is the producer of tecovirimat. These results were published independent of approval by the funding source, as stipulated by the contract. Revision accepted for publication 18 October 2014. Ó The Author(s) 2014 Reprints and permission: http://www.sagepub.com/journalsPermissions.nav DOI: 10.1177/0272989X14561681
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Supplementary material for this article is available on the Medical Decision Making Web site at http://mdm.sagepub.com/supplemental. Address correspondence to Ellie Graeden, PhD, Gryphon Scientific, 6930 Carroll Ave, Suite 810, Takoma Park, MD 20912, USA; telephone: (301) 270-0645; fax: (301) 270-0673; e-mail: ellie@gryphonscientific .com.
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by the US government) and a range of public health response characteristics that would alter the effectiveness of the public health response associated with their administration. The goal of this analysis is to compare the various public health response options to better inform the development of empirically derived emergency response plans. We have developed a simple decision support graphic designed to translate the outputs of this model for use by public health emergency planners. This analysis provides the first example of a data-driven decision support tool designed to translate the results of a comparative epidemiological modeling analysis into operations-focused information for public health emergency personnel. Uncertainty in Public Health Response Modeling An effective prophylaxis campaign requires that a significant percentage of the population receive the prophylaxis. However, coverage is a large source of uncertainty in modeling the efficacy of the public health response. There are no data available from recent outbreaks to assess the likely coverage of the smallpox vaccine (known to cause rare but severe adverse events) in the contemporary population. Similarly, there are no data available to suggest what percentage of the population would accept administration of an antiviral, such as tecovirimat, as prophylaxis. Even in high-risk, postevent scenarios in the past decade, the success of large-scale prophylaxis campaigns with either vaccines or antibiotics has been plagued by low coverage and compliance.1,2 Quantifying the contagiousness of variola in the contemporary population is also a major challenge plagued by significant uncertainty. This parameter is defined by the number of new infections transmitted by a smallpox patient over the course of his or her illness and reflects a combination of many factors. These factors are contingent on the biological characteristics of the virus as well as the immunological status, living conditions, and social interactions of the infected population. Therefore, smallpox contagiousness may be quite different in the contemporary population than in populations affected by the disease prior to its eradication. Epidemiological Modeling of Smallpox Under highly uncertain conditions for which there are little or no contemporary data available, epidemiological modeling is a powerful method to test public
health response plans against a wide range of possible scenarios. (While this model could not, therefore, be validated against event-specific data, the parameters were based on the best available scientific data for comparative studies, whether medical countermeasure efficacy studies or public health response studies for other diseases and types of response.) Computational modeling of smallpox has been used previously to compare various vaccination strategies and evaluate the relative importance of different aspects of the public health response (e.g., speed of detection, role of social structure, and value of social distancing).3–7 These studies have primarily focused on vaccination strategies or have analyzed specific aspects of the disease dynamics of naturally occurring outbreaks. For example, Kaplan et al.5 compared postevent mass vaccination with trace vaccination, and Meltzer et al.6 compared a quarantine strategy with a vaccination strategy. Additional models developed by Halloran et al.3 and Burke et al.4 used social networks of locations, including households, schools, and hospitals, to model the infection patterns and scale of outbreaks. Smallpox models such as those described by Eichner8 and by Riley and Ferguson9 analyzed contract tracing as a method of administering vaccine to contain a contemporary outbreak but with an initially infected population of 100 people or fewer. In only one prior study has the efficacy and effectiveness of tecovirimat been analyzed in the context of a smallpox outbreak. In this study, Finin et al.7 developed a model of the effectiveness of the public health response to a smallpox outbreak using vaccination with modified vaccinia Ankara (MVA) vaccine combined with tecovirimat postexposure prophylaxis or treatment. Finin et al. focused on the role of patient compliance on the overall efficacy of the public health response to a smallpox outbreak. While the study presents a careful analysis of the role of patient compliance on the efficacy of countermeasures in limiting an outbreak, this factor is not under the control of the public health community and cannot be used to support decision making in public health preparedness and response. Modeling for Public Health Decision Makers The model presented here is specifically designed to address the gaps in the previous smallpox models by assessing the value of tecovirimat in the prophylaxis and treatment of smallpox compared with a public health response based solely on vaccination. Using our smallpox model, we have explored the effect of uncertainty regarding contagiousness and
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Figure 1 Transition of the population through the incubation period when modeled as 12 single-day periods. Modeling the incubation period in 12 steps yields a distribution of cases (solid line) most similar to that of the human disease course (vertical bars). The distribution of cases as a function of the number of days spent in the incubation period is shown as modeled in a single-step (dotted line), two-step (dashed line), or 12-step (solid line) incubation period compared with the distribution of empirical data from reports of the human disease course.10,11
prophylaxis coverage on the relative value of vaccination and tecovirimat as prophylaxis and treatment administered in response to a large-scale outbreak. We present an in-depth analysis of the parametric effect of contagiousness and prophylaxis coverage on a smallpox outbreak and provide an evidencebased decision support tool that can be used to help inform decisions in public health preparedness and response, a critical downstream application of this type of analysis. METHODS Model Framework The model we developed is an expanded SEIR (susceptible-exposed-infectious-recovered) compartmental system of ordinary differential equations describing a large-scale smallpox outbreak in New York City (see Figure 2). To more accurately model the severity of the disease and efficacy of medical countermeasures, the population is divided into subpopulations based on immune status (normal, prevaccinated, and immunocompromised) and disease type (ordinary, modified, and hemorrhagic). The results of the model establish the relative effectiveness of various combinations of medical
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countermeasures administered as prophylaxis or treatment during a smallpox outbreak, as well as the public health responses necessary to disseminate those countermeasures to the affected population in reducing morbidity and mortality. The parameters were developed from empirical evidence in the published literature. The values associated with the population-level transmission of disease and the public health response were established based on a literature review and analysis of the data from previous smallpox outbreaks supplemented with data from outbreaks of diseases for which there have been more recent outbreaks, such as influenza and meningitis. Vaccine efficacy was based on the extensive data collected during the eradication campaign in the middle of the 20th century. The efficacy of tecovirimat was evaluated using data from disease in animal models infected with orthopoxviruses that most closely recapitulate the human disease course. Each parameter is incorporated in the model as a constant or variable in the differential rate equations that define movement between each stage of the disease course. After the initial population is infected, subsequent infection of the susceptible population is determined by the force of infection, defined as the rate susceptible individuals become infected. Contagiousness is approximated as the R0 distributed over the length of the contagious period based on the viral shedding rate for each disease stage. Once infected, the incubating population either continues onto each subsequent day of the incubation period or is administered prophylaxis. The population receiving prophylaxis is limited by the rate at which vaccinations can be administered during a public health response. The incubation period is divided into 12 single-day time steps through which the population moves sequentially. The population experiencing the ordinary or modified disease type then progresses into the prodromal stage of the disease. The fraction of the population experiencing hemorrhagic disease moves into a parallel path for the symptomatic stage in which they can receive treatment if not contraindicated. In the hemorrhagic form of disease, fever and rash occur simultaneously and are modeled accordingly. Those receiving treatment (all those not contraindicated) move into parallel paths based on their disease type with reduced levels of contagiousness. The reduction in contagiousness is based on the percent reduction in viral shedding by treatment with tecovirimat. After completing the disease course, each subpopulation moves into either the dead or recovered categories based on case fatality rates for
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Figure 2 Model framework shows the smallpox disease course and interactions between contagious and susceptible populations. Model framework outlines the disease course and available medical countermeasures. The solid lines indicate the flow of the population through the smallpox disease course. Patients with ordinary and modified smallpox flow through the fever and overtly symptomatic or rash stages. Hemorrhagic patients flow through a single symptomatic, contagious period (‘‘Hemorrhagic’’). The paths describing prophylaxis or treatment are opened at the onset of the public health response. All those receiving effective prophylaxis become protected. All those eligible for treatment move into a late disease stage corresponding to rash and then to dead or recovered based on treatment efficacy. Dotted lines represent the interaction of contagious populations with the susceptible populations, which determines the rate of new infections and corresponding flow into the incubation period.
each combination of disease type and subset of the population. The paths for prophylaxis and treatment become available only once the outbreak has been recognized and the medical countermeasures (MCMs) have been made available to the population. See the technical appendix in Additional File 2 for a detailed description of the equations and modeling methods. Parameters Disease Course We modeled the 3 primary clinical forms of smallpox: ordinary, hemorrhagic, and modified. In ordinary smallpox, the asymptomatic incubation stage lasts an average of 12 days and is followed by a 3day prodromal stage marked by fever.12–17 The overtly symptomatic (rash) stage is characterized first by rash and then by the eruption of pox or pustules. This stage typically lasts 8 to 11 days, ending with either death or recovery.12,13 Hemorrhagic smallpox has a case fatality rate (CFR) of 95% and primarily affects pregnant women and infants18; we assume the entire immunocompromised population (as defined in Appendix 1) would be similarly affected. Ordinary smallpox has a 30% CFR and affects the majority of the population.12,13 The modified form has a CFR near zero and primarily affects those with
partial resistance from previous vaccination. The distribution of the population between these subpopulations and their relative likelihood of contracting smallpox is described in detail in the technical appendix in Additional File 1. The transition of the population through the incubation period is modeled not as one 12-day stage but as 12 stages, each lasting one day. This division of the incubation period corrects the overestimation of the rate of transition for the majority of the population that occurs with a single, exponentially distributed incubation stage (see Figure 1).19 Medical Countermeasure Efficacy None of the MCMs against smallpox currently stockpiled by the US federal government, including ACAM2000 and tecovirimat, have been tested against the disease in humans. The efficacy of the vaccine, ACAM2000, in preventing infection is based on earlier vaccines.12,20 The MVA vaccine, intended for use in populations contraindicated for ACAM2000, requires 2 doses at a month interval and does not provide maximum protection until 6 weeks after the first dose, so while the vaccine may have some benefit, it would likely have limited utility during a postevent public health response and is not included here.21 ACAM2000 is modeled as 98% effective at preventing the onset of symptoms if administered prior to
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infection and as 54% effective at preventing the onset of symptoms if administered in the first 8 days of the incubation period.12,13,22,23 The efficacy of tecovirimat both as prophylaxis in preventing the onset of symptoms or as treatment in preventing fatalities is extrapolated from animal models of lethal orthopoxvirus infection.24–27 The efficacy of the antiviral as prophylaxis was tested in nonhuman primates infected intravenously with monkeypox (the animal model most similar to the ordinary smallpox disease course in humans). The antiviral was administered immediately after intravenous injection of the virus, which marked the onset of infection, and on days 1, 2, and 3 postinfection.24 In all cases, prophylactic treatment (days 1 and 2 postinfection) prevented both disease and death in 100% of treated animals (6/6 monkeys), while 0% (0/3) mock-treated monkeys survived. Because only 6 animals were used in this experiment, this assay could not distinguish between a countermeasure that was only 89.1% effective (89.1% is the smallest probability of individual survival resulting in an expected survival of all 6 monkeys slightly more than 50% of the time) v. one that is 100% effective. To be conservative, we therefore assumed that the countermeasure has the least possible efficacy given the number of animals in this experiment. Based on data from a study that established tecovirimat efficacy for mice with varying levels of partial immune deficiency, treatment prevented both disease and death in 100% of animals when administered on the same day as infection (30/30 mice).26 On the basis of these data, we assumed the same level of tecovirimat prophylaxis efficacy (89.1%) for the immunocompromised population as for the normal and prevaccinated subsets of the population. Because the onset of the prodromal period is defined by the onset of symptoms (fever), efficacy during prodrome is defined by prevention of mortality, not morbidity. In nonhuman primates infected with monkeypox, fever is first detected 3 days postinfection.24 Therefore, we included in our analysis only the data that describe the efficacy of tecovirimat administered on the third day postinfection to monkeys infected intravenously with monkeypox. Treatment on day 3 postinfection was 100% effective in preventing mortality (15/15 animals tested in 2 studies with 0/6 mock-treated animals surviving).24,25 Therefore, we assumed that antiviral treatment during prodrome is 95.5% effective in preventing mortality when adjusted to account for the small sample size (reduced from 100% to account for the
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fact that only 15 animals were tested). Similarly, the efficacy was determined by the most conservative estimate calculated on the basis of the number of animals tested. In immunocompromised mice, the survival rate dropped to 80% when treatment was postponed until 3 days after infection.26 Therefore, we assumed that the efficacy of tecovirimat treatment during prodrome of the immunocompromised population is 80%. The ‘‘rash stage’’ is characterized by the onset of lesions, which occurs 4 days postinfection in monkeys infected with monkeypox intravenously.24 Antiviral treatment starting 4 days postinfection has varying results depending on dosage.27 We assume that the drug will be administered at ~6 mg/kg (400 mg/70 kg adult),25 a dosage at which the drug was 89% effective when administered 4 days postinfection. Therefore, we assume that antiviral treatment on the first day of the rash stage is 89% effective. Tecovirimat can be administered either orally by pill or by intravenous injection (IV); the oral form has completed a phase II clinical study published with the Food and Drug Administration.27 Based on data suggesting that the blood level concentrations are comparable between the 2 routes of administration, we assumed no difference in the efficacy or rates of adverse events between the 2 methods.28 We assume no contraindications for vaccination based on the Centers for Disease Control and Prevention (CDC) response plans for postevent vaccination.29 There are no known contraindications for tecovirimat; however, we excluded people unable to swallow pills from the population eligible for oral administration of the antiviral.30–32 Public Health Response We model the public health response to a smallpox outbreak in New York City. The model outbreak is initiated when the first person becomes infected with smallpox. Importantly, the goal of this work is to model the current, planned public health response to a smallpox outbreak (vaccination) to a response bolstered by the use of tecovirimat. While ring vaccination may be considered at the outset of an outbreak, a rapid accumulation of new patients seeking care who have no obvious connection to each other would suggest that a large-scale release of virus had occurred. With a very large number of infections likely, and without additional information about the source of the infections, such a large influx of unrelated patients would quickly overwhelm the ability to trace all the contacts for these patients in a short period of time. Therefore, ring
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vaccination is an unlikely scenario in a contemporary, large-scale outbreak. We modeled a postevent region-specific mass vaccination campaign, as recommended by the CDC for large-scale outbreaks and shown to be most effective in earlier modeling efforts.5,33 On the basis of these references, we assume that vaccinations and oral antiviral will be administered to all those eligible in the affected region from points of dispensing/vaccination managed by the federal government, deployed once the outbreak has been recognized.5,33 The range of possible rates of administering vaccinations or coadministering vaccinations and oral antiviral prophylaxis is based on data from the City Readiness Initiative, simulated smallpox vaccination clinics, and actual public health responses to meningitis and influenza outbreaks.1,34–36 A public health response is initiated only once the outbreak is recognized and the necessary MCMs have been transported to the site of the outbreak. In the 2003 monkeypox outbreak in the United States, response was not initiated until 20 cases were seen in area hospitals.37 In our model, we assume a somewhat more optimistic scenario in which the outbreak will be recognized and a large-scale public health response mounted once 10 cases reach the fulminant stage (concomitant with presentation of pox). A sensitivity analysis of the case delay, ranging from 1 to 50 fulminant cases, was completed and is presented in Appendix 3. Defining this delay in cases (the ‘‘case delay’’) instead of days automatically corrects for a reduction in the recognition delay during larger outbreaks. The recognition delay is defined by the amount of time between when the first symptomatic smallpox patient arrives for care and when he or she is first correctly diagnosed (we assume that smallpoxspecific treatment will be administered only once the patient has been diagnosed with the disease). The case delay will be shorter for larger outbreaks, if calculated based on the number of symptomatic patients seeking medical care. The delay in mounting an effective and disease-specific response is modeled by the ‘‘response delay,’’ defined by the time estimated by the CDC for distribution of supplies from the Strategic National Stockpile.38 We assume a 2day delay before the necessary supplies are delivered from the Strategic National Stockpile and the mass prophylaxis campaign is initiated. A sensitivity analysis was completed and included in Appendix 3. Complete prophylaxis (100% coverage and compliance) of the population within 25 days was assumed as the baseline for mitigation scenarios, but the full
extent of coverage achieved is explored in this analysis. As our model attempts to quantify the theoretical maximum effectiveness of medical countermeasures, we also assume that medical countermeasures will be unlimited in supply. Any limitation under mass prophylaxis would affect the outcome similarly to reductions in prophylaxis coverage rates in the population. Contagiousness The contagiousness of a disease is often quantified as the basic reproductive number, R0, defined as the expected number of secondary infections caused by a single case introduced into a completely susceptible population. Previous studies falsely assumed a large part of the R0 of smallpox was due to infectiousness during the prodromal stage of the disease rather than during the symptomatic stage.39 To more accurately represent contagiousness, we approximated contagiousness as a function of previously published R0 values for smallpox but distributed over the disease course based on viral shedding rates extrapolated from a combination of animal and human studies.40,41 The amount of virus shed by an infected patient is an indicator of his or her contagiousness, and viral shedding, unlike many of the factors affecting contagiousness, can be quantified over the smallpox disease course. Viral shedding rates, defined by the amount of virus released into the environment by an infected patient at any given point in his or her illness, vary significantly on each day of disease.40 Because data are limited for human shedding rates, macaque data were used to help determine the relative viral shedding rates for each day over the course of the disease (Appendix 1).40,41 When normalized for the differing lengths of the disease course, viral shedding peaks on the last day of fever and first day of pox and is no longer detectable by day 13 of symptomatic illness. In the absence of data describing viral shedding during prodrome in humans, we adjusted the mean viral shedding rate based on the relative length of the macaque and human prodromal periods. Previous modeling efforts and analyses of smallpox outbreaks suggest a wide range for the possible R0 of smallpox. The R0 has most often been estimated to be between 3.5 and 6 in contemporary populations; we assume a baseline R0 of 5 but consider a range from 1.5 to 18, with the upper limit defined by the established R0 of measles, considered the most contagious of human diseases.3,5,42–46 Tecovirimat is an egress inhibitor; treatment with the antiviral reduces viral shedding by 22-fold in animals infected with orthopoxvirus.47 Based on these
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animal data, our model thus assumed a 22-fold reduction in contagiousness in patients receiving antiviral treatment. Based on studies of contact rates in contemporary populations both under normal and epidemic conditions, contact rates and, correspondingly, contagiousness, will drop by 52.1% (from 11.5 contacts per day per person under normal conditions to 6 contacts per day per person) after a smallpox outbreak is recognized and the public health response initiated due to social distancing measures.48–51
are accurately diagnosed), treatment is administered to patients in the rash stage. Treatment significantly reduces viral shedding and therefore contagiousness; there is a corresponding reduction in caseload with the addition of tecovirimat treatment compared with vaccination-only scenarios across a range of public health response assumptions. As shown in Figure 3D, administering antiviral treatment also significantly reduces cumulative fatalities compared with vaccination-only scenarios. This reduction in mortality is largest at the height of the outbreak, around a month after the initial population is infected.
RESULTS Effect of Prophylaxis Coverage on Caseload MCM Efficacy in an Outbreak Figure 3 compares the effect of no mitigation, vaccination alone, or vaccination prophylaxis and tecovirimat treatment on morbidity and mortality for each day of a smallpox outbreak with 1000 people initially infected. Figure 3A,B shows an unmitigated disease scenario and both mitigation scenarios, and Figure 3C,D shows only the mitigated scenarios. Caseload is defined by the number of people reaching prodrome, which marks the onset of symptoms and the beginning of the contagious stage of disease. The results shown here are based on scenarios assuming 100% prophylaxis coverage of the population with an R0 of 5 (with contagiousness distributed proportionally to viral shedding rates over the contagious period) and are consistent across scenarios based on a range of public health assumptions (data not shown). The effect of these assumptions is considered in detail in the remainder of this study. As shown in Figure 3A,C, any mitigation, both vaccination alone as well as vaccination and tecovirimat treatment, greatly reduces the effects of the epidemic. Vaccination alone reduced the total morbidity of the epidemic from 13.7 million cases to 2861, while treatment in addition to vaccination further reduced morbidity to 1961 cases. Similarly, vaccination alone reduced the total mortality from 4.9 million deaths to 1160, and vaccination plus treatment further reduced the death toll to 126. For mitigation scenarios, shown in Figure 3B, the number of new cases per day increases over the first 2 weeks as those initially infected with smallpox become symptomatic, at which point they become contagious and begin infecting others. The number of new cases per day drops before the second wave of patients moves from incubation into prodrome. Once the public health response is initiated (after 10 cases begin exhibiting the hallmark symptom, pox,
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The extent to which a mass vaccination campaign can reach all susceptible people is unknown. To address this uncertainty, we calculated the effect of prophylaxis coverage rates on the ability of vaccination alone and vaccination prophylaxis with tecovirimat treatment to control an outbreak. As shown in Figure 4, the percentage of the population receiving effective prophylaxis has a significant, nonlinear effect on the total caseload during an outbreak with 1000 initial infections. The total caseload increases dramatically in vaccination-only scenarios when less than 80% of the population receives prophylaxis. When 50% of the population receives prophylaxis, the outbreak is limited in size only by the total number of people in the initial susceptible population. By contrast, vaccination prophylaxis and tecovirimat treatment successfully control the outbreak unless prophylaxis coverage drops to 20% or less. (An outbreak is considered controlled when the secondary cases outnumber primary cases by less than 10 to 1.) Tecovirimat is effective as prophylaxis throughout the incubation stage (in comparison to vaccination, which is effective only early in the incubation period), and coadministering the antiviral with vaccination as prophylaxis also reduces total morbidity and mortality but to a lesser extent (data not shown). The results here include only vaccination; these results are not significantly affected when tecovirimat is additionally administered as prophylaxis (data not shown). Effect of Contagiousness on Caseload The contagiousness of smallpox in a modern outbreak is highly uncertain. To address this uncertainty, we compared the effect of a wide range of contagiousness on the size of outbreaks in which
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Figure 3 Tecovirimat treatment significantly reduces both morbidity and mortality. Results shown from model scenarios with 1000 initial infections, an R0 of 5, and 100% prophylaxis. Scenarios considered include those in which vaccine alone is administered as prophylaxis (solid lines), vaccine is administered as prophylaxis and tecovirimat as treatment (dashed lines), and no mitigation (dotted lines). (A) The number of new cases reaching the prodromal stage (symptomatic and contagious) is shown for the 2 mitigation and the no-mitigation scenarios. (B) The number of new cases reaching the prodromal stage (symptomatic and contagious) is shown for the 2 mitigation scenarios only. (C) The number of fatalities is shown for the 2 mitigation and the no-mitigation scenarios. (D) The number of fatalities is shown for the 2 mitigation scenarios only.
Figure 4 Prophylaxis coverage has a large, nonlinear effect on caseload. The total number of cases from outbreaks with 1000 initial infections is shown on a log scale for scenarios in which the percentage of the population receiving vaccine prophylaxis ranges from 100% to 0%. Caseloads for outbreaks in which vaccine prophylaxis alone is administered are shown with a solid line; caseloads for outbreaks with vaccine prophylaxis and tecovirimat treatment administered are shown with a dashed line; caseloads for outbreaks with no mitigation are shown with a dotted line. The total population is marked with a double solid line.
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100,000,000
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Ro Figure 5 Contagiousness has a large, nonlinear effect on caseload. The total number of cases in outbreaks with 1000 initial infections is shown on a log scale based on scenarios with contagiousness parameters based on R-values ranging from 1.5 to 18. Caseloads for outbreaks in which vaccine prophylaxis alone is administered are shown with a solid line; caseloads for outbreaks with vaccine prophylaxis and tecovirimat treatment administered are shown with a dashed line; caseloads for outbreaks with no mitigation are shown with a dotted line. The total population is marked with a double solid line.
vaccination alone was administered or both vaccine prophylaxis and tecovirimat treatment were administered. As shown in Figure 5, the caseload of an outbreak is also highly sensitive to the relative contagiousness of the virus, modeled by distributing R0 proportionally over the disease course (see Methods). In postevent vaccination scenarios assuming that 50% of the population receives effective prophylaxis but no treatment is available, the outbreak infects at least 10-fold more victims than were initially infected when the R0 is just over 3 or higher. In scenarios with antiviral treatment administered in conjunction with vaccine prophylaxis, the outbreak is controlled (fewer than 10,000 total cases) as long as the R0 is 7 or less. The effect of contagiousness on the caseload in these outbreaks is consistent whether vaccination alone or vaccination and tecovirimat are administered as prophylaxis (data not shown). Outbreak Control Considering Both Prophylaxis Coverage and Contagiousness As shown in Figure 6, we determined the interaction between disease contagiousness and prophylaxis coverage to identify conditions under which vaccination alone is sufficient to control an outbreak
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and when tecovirimat treatment is required. The heat map shows the percentage of the population receiving prophylaxis on one axis and the relative contagiousness of the virus on the other. The map highlights conditions under which the outbreak is controlled by prophylaxis alone, is contained by prophylaxis plus treatment, or is uncontained (as described above, an uncontained outbreak is one in which secondary cases outnumber primary cases by 10 to 1). At high levels of prophylaxis coverage and low contagiousness, vaccination alone is sufficient to control the modeled outbreak. However, there are a large number of plausible scenarios under which tecovirimat treatment is necessary to control the outbreak. Outbreaks of a highly contagious virus in which less than 70% of the population receives prophylaxis are not controlled even when both vaccine prophylaxis and antiviral treatment are administered. Including tecovirimat as prophylaxis does not affect these breakpoints (data not shown). CONCLUSIONS With the addition of tecovirimat to the Strategic National Stockpile, the United States has, for the first
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Figure 6 Heat map showing the relative importance of prophylaxis coverage for outbreaks with virus of varying levels of contagiousness. Heat map is coded by whether the smallpox outbreak is uncontrolled, where an uncontrolled outbreak is one in which secondary cases outnumber primary cases by 10 to 1 (e.g., more than 10,000 for outbreaks with 1000 people initially infected). Outbreaks in which vaccine prophylaxis alone controls the outbreak are shown in light gray; outbreaks in which adding tecovirimat treatment is sufficient to control the outbreak are shown in dark gray; outbreaks in black are not controlled even with both vaccine prophylaxis and treatment administered.
time, an effective treatment for smallpox. The effect of uncertainty regarding prophylaxis coverage rates or viral contagiousness on the value of this antiviral in mitigating an outbreak has not previously been determined. The analysis presented here addresses the efficacy of tecovirimat in the treatment of smallpox when coadministered with the vaccine considering these sources of uncertainty. The results presented here suggest that both prophylaxis coverage of the population and contagiousness have a large, nonlinear effect on the size of a smallpox outbreak. With an R0 of 5 and no treatment, prophylaxis coverage of the population must be 80% to control the outbreak, whereas when tecovirimat treatment is included, the outbreak is controlled with only 30% prophylaxis coverage. Prophylaxis coverage of previous vaccination campaigns, even for highly contagious, highly deadly diseases in populations with few contraindications, has been as low as 50% (such as during the meningitis outbreak on the Michigan State University campus in the early 2000s).1 Vaccination compliance rates in a mock smallpox-vaccination exercise in San Francisco were also near 50%.35 Taken together, these data suggest that the proportion of the population receiving prophylaxis could well be less than 80%,
and tecovirimat treatment would be required to control the outbreak. As described here, our results suggest that, assuming 50% prophylaxis coverage, vaccination alone can control the outbreak only if the R0 is less than 4. If the R0 is greater than 4, tecovirimat treatment is required to control the outbreak. Neither measure is sufficient to control outbreaks in which the R0 is greater than 7. A rigorous analysis of historical outbreak reports from Europe over the past few centuries calculated the likely R0 of smallpox as between 3.5 and 6, and these authors suggest that these values may be an underestimate of the contagiousness of smallpox in a contemporary outbreak due to increases in population density and a lack of herd immunity.42 Under such conditions, tecovirimat treatment administration in conjunction with vaccine prophylaxis is required to control the outbreak. The results of this study suggest that including an effective treatment in the public health response to a large-scale smallpox outbreak significantly expands the range of outbreak scenarios that can be controlled with the current medical countermeasures available. There is great uncertainty surrounding the epidemiology of smallpox and the ability of public health to vaccinate all susceptible people in an outbreak.
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These data provide the evidence basis for effective decision making when developing emergency public health plans for a contemporary smallpox outbreak.
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ACKNOWLEDGMENTS We thank Rocco Casagrande and Mark Kazmierczak for their contributions to and review of both the model and manuscript and Anna Kushnir for her review and editing of the manuscript.
20. Nalca A, Zumbrun EE. ACAM2000: the new smallpox vaccine for United States Strategic National Stockpile. Drug Design Dev Ther. 2010;4:71–9. 21. Henderson DA. Smallpox virus destruction and the implications of a new vaccine. Biosecur Bioterror. 2011;9(2):163–8.
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