641

MODERN VACCINES Immunisation and herd immunity

development of a safe, effective, and cheap vaccine is the first step-albeit a vital one-towards control of an only infectious disease within a community. The dynamics of the interaction between a population of hosts and an infectious agent is inherently non-linear (for instance, when population density doubles the prevalence of infection will usually increase more than two-fold), and complex patterns of temporal changes in the incidence of infection can arise when immunisation programmes with partial coverage are initiated. This paper sketches how mathematical models that are soundly based on epidemiological data can help us understand the effects upon population-level or "herd" immunity of specific immunisation policies. Some of the questions that can be illuminated within such an analytic framework are: What proportion of the population should be immunised to achieve eradication (locally or globally)? How is this affected by birth rates and other demographic factors? What is the best age to immunise? How does mass immunisation affect the age distribution of susceptible individuals, particularly in those age-classes most at risk from serious diseases? How significant are genetic, social, or spatial heterogeneities in susceptibility or exposure to infection? And how does this affect herd immunity? The

Reproductive

rate of an infection

A central concept is that of the basic reproductive rate of the infection, Ro.1-3 For most viral and bacterial infections and many protozoan ones, Ro is the average number of secondary cases produced by one primary case in a wholly susceptible population. Clearly, an infection cannot maintain itself or spread unless Ro is larger than one. Since Ro will usually increase as host population densities increase (or, for sexually transmitted diseases, as rates of acquiring new sexual partners increase), the criterion Ro > 1 translates into a requirement that population densities (or rates of partner acquisition) exceed some threshold value. Bartlett4 and Black,s for example, have shown that populations of 400 000-500 000 or more are needed within island or city communities for endemic maintenance of measles. Indeed, most directly transmitted viral and bacterial infections of childhood-of the kinds that wrought such havoc when introduced from the crowded Old World into the sparsely settled New World Oceania-have high threshold densities and probably appeared in human populations only when agriculture began some 10 000 years ago. By the same token, the different rates of spread of human immunodeficiency virus (HIV) among homosexual males in large cities in the US and Europe, heterosexuals in Africa, and heterosexuals

in developed countries are roughly consistent with estimated differences in rates of partner acquisition (and thus differences in Ro between and within these various

groups).6 For a specific infection, Ro may be roughly estimated as Bf(A-D).3,H Here B is the reciprocal of the per capita birth rate (which would equal the average life expectancy if birth rates and death rates were equal), A is the average age at which infection is acquired (before any immunisation programme), and D is the characteristic duration of protection by maternal antibodies. More exact estimates, based mainly on age-specific seroprevalence, are listed in the table for various infections in particular communities. The Ro values depend on social and behavioural factors (which influence contact rates and thence A), on the biology of the infectious organism and the host (which influences D and A), and on the demography of the population (the value of B)--hence the variation seen in the table. Eradication and herd immunity Other things being equal, the larger the value of Ro, the harder it will be to eradicate the infection from the community in question. In a "homogeneously mixed" population, eradication will be achieved if the proportion successfully immunised, p, exceeds a critical value pe 1-1/R.t Thus the larger R, the higher the coverage needed to eliminate the infection. As discussed below, a =

*In

a steady, endemic state, each primary case produces, on average, one secondary case. That is, the effective reproductive rate, R, is R= 1. This happens because the basic reproductive rate, R,,, has to be discounted, since many of the contacts have already expenenced infection, and are now recovered and immune. Roughly speaking, in a homogeneously mixed population, R" is discounted in proportion to the fraction of the population remaining susceptible, x: R = R"x = 1. Thus R" can be estimated as 1 /x, where the fraction susceptible, x, can be estimated accurately from serological studies. Very roughly, if people live an average of L years, become mfected at age A, and are protected by maternal antibodies up to age D, we see that x (A-D)/L. But in a growing population, the relevant estimate of L is B, the reciprocal of the per capita birth rate, not the inverse of the death rate. Hence the estimate R. - B/-(A-D).

tTo eradicate infection, the effective reproductive rate, R R"x, must be brought below unity. But ifa proportion, p, are successfully immunised, then x < 1-p. Hence the rough formula p;; 1-1/R0. =

=

ADDRESSES. Biology Department, Imperial College, London SW7 2BB, UK (Prof R M Anderson, FRS); Zoology Department, Oxford University, and Imperial College, London, UK (Prof R M. May, FRS) Correspondence to Professor Anderson

642

SOME EPIDEMIOLOGICAL PROPERTIES OF VACCINE-PREVENTABLE CHILDHOOD VIRALAND BACTERIAL INFECTIONS

Source, refs 7-9

estimate of pc, must take account of age-specific effects in transmission efficiency and other forms of genetic and social heterogeneity.,9 The rough estimate, however, is usually a good guide. Thus-political questions asideglobal eradication of measles, with its Ro of 10 to 20 or more, is almost sure to be more difficult than was eradication of smallpox, with its estimated Ro of 2 to 4.3,7 The comparison between measles and rubella in the US provides another illustration: rubella (A around 9 years before immunisation) has an Ro value roughly half that for measles (A around 5 years before immunisation), and indeed rubella has been effectively eradicated in the US (where mumps/measles/ rubella, MMR, vaccination is essentially compulsory) while the incidence of measles has declined more slowly and continues to show local flare-ups. Why do we not require 100% coverage to eradicate an infection? Immunisation has both a direct effect and an indirect effect. The direct effect is to protect those successfully immunised; but, from the viewpoint of the infection, the host population is now effectively smaller and transmission is correspondingly less efficient. It follows that the effective population density of hosts will fall below threshold, and the infection will be unable to maintain itself, at some immunisation coverage short of 100%. Mass immunisation at levels below those needed to eradicate infection obviously reduces the total number of cases. Perhaps surprisingly, both theory8,9 and observation 10 suggest that it has little impact on the total number of individuals remaining susceptible.t Detailed serological data based on large samples and finely stratified by age (horizontal data), sex, and geographical region, collected before and repeatedly during (longitudinal data) the implementation of the vaccination programme, are of particular importance in assessing such effects. Their collection, analysis, and interpretation should be a central part of any programme of mass immunisation.8 The indirect effect of a programme of immunisation at below-eradication levels is, as we have just seen, to bring the probability of an unimmunised individual acquiring infection below what it would have been in the absence of any immunisation. A corollary of this indirectly diminished probability of infection is that those fewer individuals who do experience infection are infected at an older average age. If the risk

more exact

tSo long as the infection remains endemic the effective reproductive rate will obey R=R0X=1. That is, x = 1/R01, the fraction remaining susceptible, depends only on R, and not on whether those losing susceptibility did so as a result of immunisation

or

of natural infection.

Fig 1-lmpacts of two different immunisation programmes on herd immunity to rubella virus (proportion of the population by age with antibodies to the virus). (a) Cross-sectional profiles of rubella antibodies in females and males (combined) in South Yorkshire 1969-85." Rubella immunisation of teenage girls was introduced in 1980; the profiles are similar in pre and post vaccination years. (b) Finland.12 in the period 1980 to October, 1982, vaccination was targeted at girls 13 yr of age but in November, 1982, MMR vaccine was administered to boys and girls of 14-18 mo and 6 yr.

associated with infection increases with age, such a programme of immunisation at levels below eradication can therefore have perverse consequences.

Risks to the unvaccinated Rubella provides an example of the down-side of vaccination. The concern here is not so much with the infection itself, but with the possible damage done to babies whose mothers contract rubella in the first trimester of pregnancy (congenital rubella syndrome, CRS). A programme that succeeded in vaccinating, say, 50% of all 2-year-olds would, on the one hand, reduce the total number of cases of rubella, but on the other hand would push the average age of the smaller number who are infected towards the child-bearing years. Intuition suggests that, if very high levels of coverage can be attained (under compulsory programmes, as in the US), eradication can be achieved by vaccinating successive cohorts of 2-year-olds. Conversely, if vaccine uptake is 60-70% under a voluntary scheme (as in the UK), intuition suggests that vaccination should be confined to 13-year-old girls, so that infection can spread and confer immunity at younger ages (fig 1, a). But simple intuition cannot tell us at what level of coverage to switch

643

from one strategy to the other. For such a decision, a detailed epidemiological calculation must be made; the calculations suggest that a switch to the US strategy is advisable provided that more than 60% of boys and girls can be immunised by 2 years of age.9 Similar computations can assess the probable impact on the incidence of CRS of a two-stage programme of adding vaccination of 2-year-old boys and girls to the existing vaccination of around 80-85 % of 13-year-old girls. Such additional vaccination would have little effect one way or the other unless the uptake in 2-year-olds was very high (80-90%). The two-stage programme could make matters worse unless the two arms of the programme were run concurrently for at least 10 years, with high levels of coverage at both ages.8,9 The recent history of rubella in Finland provides a more detailed impression of these complexities.11,12 In that country from 1975 to 1982, rubella immunisation was targeted at girls only in the age-range 12-18 years; such vaccination at ages later than the average age of infection (7-9 years) had little impact on overall transmission. From November, 1982, an additional programme of immunising young children in the age-range 1-6 years was introduced (MMR). As shown in fig lb, the new programme had an immediate effect on transmission rates and shifted the age distribution of cases, increasing the average age at infection. In addition, there was a pronounced ripple in the agestratified serological profile, resulting from the cohort of susceptible children who were just older than the age-range covered by the initial immunisation in 1982. The features of fig 1 are exactly as predicted by mathematical models.7,9 In developing countries, transmission rates for rubella are higher than they were in developed countries before immunisation (average age at infection 5 years or so, compared with 8-9). It follows that vaccinating 50% of all 2-year-olds against rubella could double the incidence of CRS in such countries.8,9 Switching from measles vaccine to MMR is clearly not a good idea in these circumstances. Broadly similar considerations arise whenever we are planning an immunisation programme with incomplete coverage against an infection where the risk of serious complications increases with age. For poliomyelitis, the risk of paralysis does so increase. It is disconcerting that programmes of polio immunisation, often with modest levels of coverage, seem to have been implemented in some developing countries without attention to such worries. Fortunately, our calculations suggest that the age-specific risk of paralytic complications is such that the net incidence of paralytic complications declines slightly, even when the coverage is low. This particular example, along with those of rubella and mumps, highlights the necessity of acquiring detailed age-stratified data on the incidences of serious diseases arising from infection. Such data must be defined as risk of serious disease per case of infection (assessed from serology, not case notifications). The quantitative detail of the form of the risk-by-age function determines whether or not a particular level of vaccination coverage, over a defined band of age classes, increases or decreases the incidence of serious disease in the target population. A variation on this theme is provided by the use of chemotherapy for those infected with HIV. At present, the only drug with proven efficiency against AIDS is zidovudine, although the extent to which it prolongs life is unclear. There is current debate about licensing the use of zidovudine for symptom-free infection as well as AIDS. Although such a drug may benefit afflicted individuals, its

community-level effects could be perverse if treated people remained infectious and continued to spread infection. Widespread use of such a drug, even though it prolonged the lives of infected individuals, might actually reduce average life-expectancy within the risk-group in question (because a higher fraction ended up being infected). The optimistic view is that, since zidovudine seems to reduce detectable levels of HIV, it is also likely to reduce infectiveness. Similar concerns arise for proposed treatments termed where immunisation boosts the immune immunotherapy, system and delays the onset of disease but does not eliminate the virus from the patient, who remains infectious. More attention should be given to these questions-to the interests of the community of yet-uninfected individuals as well as HIV/AIDS patients-when chemotherapeutic or immunotherapeutic agents are being developed. It is vital to know the impact of a drug on the infectiousness of a patient, if the drug is to be used widely in a given community. Host-pathogen associations, like all other prey-predator systems, tend to exhibit oscillatory behaviour. This is best recognised in the "inter-epidemic" cycles of measles (total cases oscillating with a roughly 2-year period), pertussis (3-year period), and other childhood infections in developed countries before immunisation (see table). Immunisation programmes generally cause such cycles to lengthen. Abrupt introduction of an immunisation programme in a situation where the original inter-epidemic cycle has small amplitude can, in some instances, excite large oscillations in the incidence of infection (or of serious complications resulting therefrom), before the incidence falls to a steady and lower level or the infection is eradicated. Such oscillations, which seem to have occurred with rubella and CRS in the US and the UK,8,9 may cause alarm if the intrinsic dynamic properties of the systems are not appreciated. Incidentally, the rather ragged 2-year cycles for measles in New York City and Baltimore have been analysed in the light of contemporary notions about "chaos"-simple and completely deterministic systems that exhibit apparently random behaviour. These time-series for measles indeed seem to be generated by deterministic chaos, providing one of the best examples of the phenomenon in a natural setting. One consequence is that short-term predictions may be possible, even though the data look noisy. But all this is another, albeit fascinating, story-see Gleick.13

Population factors Among the many complications that detailed analyses must grapple with are inhomogeneities in transmission processes arising from age-related, genetic, geographical, social, or behavioural factors .7-10 As one example, consider what happens when hosts are distributed inhomogeneously in space, with some people living in dense aggregations and others isolated in groups or villages. This can lead to heterogeneities in transmission rates which, in turn, can result in the infection’s basic reproduction rate, Ro, being on average greater than suggested by estimates based on the assumption of spatial homogeneity. Under these circumstances the best solution may be to target vaccination coverage in relation to group size, with denser groups receiving the higher rates of vaccination; the optimum programme is defined as that requiring the smallest total, community-wide, number of immunisations for elimination or a defined level of control. This strategy reduces the overall proportion who must be vaccinated to achieve

644

Fig 2-Schematic age-stratified serolog icalI prof itef or measles infection in a developing country. Average age at infection, A, is 3 yr and maternal antibodies (Abs) provide protection for an average of 6 mo. In this example theory predicts that the vaccination coverage to block transmission would be greater than 98% of 1 -yr-olds. At the age of maximum susceptibility (9 mo) only 70% of children can be effectively immunised (with a vaccine that has low efficacy If maternal antibodies are present). Vaccination of the community at two ages (9 mo and 2 yr) is required m this case to reduce transmission and to widen the "age window" of susceptibility in which vaccination can occur."

Fig 3-Vaccine uptake in England by year. The figures for pertussis (pert), measles (meas), polio (pol) and diphtheria (dip) represent percentage uptake (completed primary course) by end of 2nd yr after birth. For rubella (rub) the figures represent percentage uptake by schoolgirls age 15 yr on Dec 31 of the stated year The 1987/88 figures represent children born in 1985 and vaccinated in 1985, 1986, 1987 and up to March 31, 1988. MMR vaccine was introduced in October, 1988, and provisional figures based on the Cover of Vaccination Evaluated Rapidly programme (started m January, 1987) suggest that by November, 1989, coverage for MMR was 72% and coverage for measles vaccine only (no MMR) was 14% by 2 yr of age (source, Public Health Laboratory Service Communicable Disease Surveillance

elimination, compared with that estimated on the assumption of spatial homogeneity. The conclusion has practical implications for the control of infections such as measles and pertussis in some developing countries, where rural-urban differences in population density tend to be much greater than in developed countries. What is the best age at which to immunise? The answer depends on social and economic issues as well as purely biological ones. But the biological issues can, by themselves, be formidable. In many developing countries, high rates of population growth and crowded conditions result in high transmission and low average ages at infection. Immunisation at too young an age can be ineffective if the infant is still protected by maternal antibodies, and the "age-window" between decline in maternal antibody protection and acquisition of infection is very narrow. It can even be that vaccination at a single age, even with 100% coverage, is insufficient to eradicate infection (fig 2).

Macroparasites This paper has dealt exclusively with those infections where the host populations can be divided into a small number of distinct categories-susceptible; infected-but-latent; infectious; recovered-and-immune. Most viral and bacterial and many protozoan infections are of this kind, which we call microparasites. On the other hand, for most infections by helminths and arthropod parasites one must distinguish between infection (having one or more parasite) and disease (harbouring a burden large enough to produce serious effects). The mathematical models here must deal with the full distribution of parasites among hosts, and with possibilities that egg-production, pathogenic effects on the host, evocation of a degree of immunity, and so on all depend how many parasites a host harbours; we call these infectious agents macroparasites.15 The distinction is obviously a rough schematic one, but it seems useful. For macroparasites, the mechanical models tend to be more

on

Centre)

complex and the underpinning data somewhat harder to get. But the range of issues relating to public health planning are broadly similar to those for microparasites, and appropriately constructed models can be similarly illuminating. We have given a general review of the epidemiology of macroparasites elsewhere.16

Voluntary or compulsory? In planning public health programmes the mainly biological questions we have dealt with above must be woven together with political, economic, and social considerations. With voluntary immunisation programmes (see fig 3), one difficulty is that many people recognise that the best outcome would be for everyone else to be immunised (so that the infection is eradicated) while they are not, so that they escape any possible harmful side-effects. There can be a genuine tension here between the interests of the individual and the interests of the community.17 The essential issue is closely parallel to fundamental problems in evolutionary biology, having to do with the evolution of altruistic behaviour; evolution acts on individuals, and selfish cheaters can prosper even though the group as a whole suffers. Conflicts between individual and group interests have a long history in human societies. Our remarks about rubella and CRS can be recast to say that, in an imaginary community where vaccination was possible only for girls and only at age 2 years, it is in the interests of an individual female to be immunised, but in the interests of the community that no one be immunised (because each individual thus directly protected against the possibilities of producing a CRSafflicted baby will, via the indirect effects discussed above, produce on average more than one case of CRS elsewhere in the population). This particular tension between individual and group interests is the reverse of the more familiar one.

645

Since these tensions derive from biological realities, they cannot be wished away by education programmes. If a large enough fraction of all other children are indeed voluntarily vaccinated against pertussis, parents do better to decline vaccination for their child. We believe the answer to these dilemmas, where individual and group interests ineluctably are programmes of compulsory immunisation, backed by an analytical understanding of the effects of herd immunity and by publicly funded compensation for sideeffects.

conflict,

REFERENCES 1. Ross R. Some a priori pathometric equations. Br Med J 1915; i: 546-47. 2. Macdonald G. The epidemiology and control of malaria. London: London University Press, 1957. 3. Anderson RM, May RM, eds. Population biology of infectious disease. Berlin: Springer, 1982. 4. Bartlett MS. Measles periodicity and community size. J R Statist Soc A

1957; 120: 48-70. 5. Black FL. Measles endemicity in insular populations: critical community size and its implications. J Theor Biol 1966; 11: 207-11. 6. Anderson RM, May RM. Epidemiological parameters of HIV transmission. Nature 1988; 33: 514-18.

RM, May RM. Vaccination and herd immunity to infectious disease. Nature 1985; 318: 323-29. 8. Anderson RM, May RM. Vaccination against rubella and measles: quantitative investigations of different policies. J Hyg 1983; 90: 7. Anderson

259-325. 9. Anderson RM, Grenfell BT. Quantitative investigation of different vaccination policies for the control of congenital rubella syndrome (CRS) in the UK. J Hyg 1986; 96: 305-33. 10. Fine PEM, Clarkson JE. Measles in England and Wales. II. The impact of the measles vaccination programme on the distribution of immunity in the population. Int J Epidemiol 1982; 11: 15-25. 11. Anderson RM. Populations and infectious diseases: ecology or epidemiology? J Anim Ecol (in press). 12. Ukkonen P, von Bronsdorff C. Rubella immunity and morbidity: effects of vaccination in Finland. Scand J Infect Dis 1988; 20: 255-59. 13. Gleick J. Chaos: making a new science. New York: Viking, 1987. 14. Nokes DJ, McLean AR, Anderson RM, Grabowsky M. Measles immunization strategies for countries with high transmission rates: predictions using a mathematical model. Int J Epidemiol (in press). 15. Anderson RM, May RM. Population biology of infectious diseases. Parts I and II. Nature 1979; 280: 361-67, 455-61. 16. Anderson RM, May RM. Helminth infections of human: mathematical models, population dynamics and control. Adv Parasitol 1985; 24: 1-101. 17. Nokes DJ, Anderson RM. The use of mathematical models in the epidemiological study of infectious diseases and in the design of mass immunization programmes. Epidem Infect 1988; 101: 1-20.

EPIDEMIOLOGY L-tryptophan and eosinophilia-myalgia syndrome in New Mexico

On Oct 30, 1989, the New Mexico Health and Environment Department learned of 3 patients with eosinophilia and severe myalgia who had been taking L-tryptophan. Further review of these and similar cases led to the initial recognition of the eosinophilia-myalgia syndrome (EMS) epidemic. To elucidate the apparent association between products L-tryptophan-containing (LTCPs) and EMS a case-control study was done. The case definition was unexplained peripheral eosinophilia (2000/µl or more) and incapacitating myalgia. Cases were found through review of white blood cell counts from May 1 to Oct 31, 1989, in nine medical laboratories in New Mexico. 11 cases and 22 matched controls were interviewed for information on symptoms and other clinical findings, on the use of LTCPs, and on potential confounding factors. All 11 cases (100%) used LTCPs compared with only 2 controls. These findings led to a ban on the sale of LTCPs in New Mexico, followed by a nationwide recall of such preparations in the United States.

Introduction On Oct 30, 1989, illnesses of unknown cause in 3 women from the Santa Fe/Los Alamos area of northern New Mexico involving eosinophil counts of 9145-10 402/1 were reported to the State’s health and environment department. The patients’ physicians had noted that all 3 were taking L-tryptophan. Further investigation and press coverage led to reports of additional patients in New Mexico. On Nov 7 New Mexico advised consumers to stop using L-tryptophan-containing products (LTCPs), and other State health departments were asked to look for patients. By Nov 15, the Centers for Disease Control (CDC) had

ADDRESSES: Office of Epidemiology, New Mexico Health and Environment Department, Santa Fe, New Mexico (M. Eidson, DVM, C. M. Sewell, DrPH, R Voorhees, MD); Surveillance and Programs Branch (R. M Philen, MD) and Health Studies Branch (E M. Kilbourne, MD), Division of Environmental Hazards and Health Effects, Center for Environmental Health and Injury Control, Centers for Disease Control, Atlanta, Georgia, USA. Correspondence to Dr M. Eidson, Office of Epidemiology, New Mexico Health and Environment Department, 1190 St Francis Dr, Santa Fe, New Mexico 87503, USA

Immunisation and herd immunity.

641 MODERN VACCINES Immunisation and herd immunity development of a safe, effective, and cheap vaccine is the first step-albeit a vital one-towards...
710KB Sizes 0 Downloads 0 Views