Comment
Ebola: no time to waste
18 000
Current projections R=0·9, January, 2015 R=0·9, November, 2014
Lancet Infect Dis 2014 Published Online October 24, 2014 http://dx.doi.org/10.1016/ S1473-3099(14)70851-5 See Online/Articles http://dx.doi.org/10.1016/ S1473-3099(14)70995-8
300 000
16 000 250 000 14 000 200 000
12 000 10 000
150 000 8000 100 000
6000
Cumulative incidence
4000 50 000 2000 0
31 ,2
01 6 Au g1 8, 20 16
0
Jan
The 2014 Ebola epidemic, already devastating to those countries most affected, threatens to evolve into a health and humanitarian catastrophe of historic scope.1 As infectious disease epidemiologists, we note with sadness that the epidemic has brought the notion of exponential growth into the popular sphere, with media sources buzzing with talk of basic reproductive numbers (R0).2 Indeed, the growth of this epidemic fits so well with mathematical epidemiological ideas that it seems torn from the pages of a textbook. And thus, even as the current Ebola epidemic wastes lives, devastates economies, and causes widespread fear, it follows a seemingly well behaved epidemiological process, readily understood through the use of mathematical modelling. In The Lancet Infectious Diseases, Joseph Lewnard and colleagues3 developed a mathematical model to predict the transmission of Ebola virus disease (EVD) in Montserrado County, Liberia, up to Dec 15, 2014. This region, home to Monrovia, Liberia’s capital, has been severely affected by EVD, with more than 1600 cases and 1000 deaths reported as of Oct 14, 2014.4 The authors used their model to assess the effectiveness of three interventions to control the Ebola outbreak: allocation of additional beds by construction of EVD treatment centres; acceleration of case ascertainment; and distribution of protective kits for home care for all newly ascertained cases. With epidemiological data, Lewnard and colleagues estimated the R0 of EVD to be 2·49 (95% CI 2·38–2·60). With their mathematical model, they predicted that expansion of the capacity of EVD treatment centres alone is not nearly as effective as coupling it with more rapid case ascertainment, because ascertainment reduces the infectiousness of cases. For example, providing 2400 beds over a period of 2 weeks, while concurrently accelerating case ascertainment five-fold, was projected to avert 62 220 (53 556–70 654) EVD cases by Dec 15, 2014. Of note, these bed numbers for EVD treatment centres are optimistic: the bestcase scenario assumes up to 4800 beds available by Dec 15, 2014, but as of Oct 15, 2014, Liberia reports that only six of 28 planned EVD treatment centres are
Incident cases (per 15 day generation)
William Shakespeare, King Richard II
operational, providing 620 of 2930 planned beds.5 Provision of protective home care kits became an important strategy in the model when beds at EVD treatment centres were not available. For example, distribution of kits to households of ascertained cases for whom no beds are available is projected to avert between 4497 (95% CI –5153 to 13 524) and 30 557 (22 535 to 38 663) cases, by Dec 15, 2014, corresponding to intervention efficacy ranging from 10% to 50%. Perhaps the most striking result of this study is the importance of timing of intervention rollout on projected disease dynamics. Lewnard and colleagues show that if all three interventions were initiated 2 weeks earlier than in the base case (ie, Oct 15, 2014, rather than Oct 31, 2014), up to 137 432 (129 736–145 874) cases of EVD could have been averted, compared with up to 97 940 (90 096–105 606) cases. Of course, by the time this report is published, Oct 15, 2014 will be a historical date, but the key takehome message for readers is this: we have no time to waste. The urgency of timely intervention in the Ebola epidemic cannot be overstated. The reason is one of
No v2 2, 20 13 Ju ne 10 ,2 01 4 De c2 7, 20 14 Ju ly 15 ,2 01 5
“I wasted time, and now doth time waste me”
Figure: Projected course of the 2014 Ebola epidemic using the IDEA model The projection is based on global case count data to Oct 18, 2014.6 Dark green curves represent projections under the current level of control (solid curve represents incidence, dashed curve represents cumulative incidence). Corresponding red and blue curves represent projections in the face of a decline in reproductive number after control (R) to 0·9 by January, 2015, or November, 2014, respectively. Model parameters: R0=1·858, d=0·009954 (d is a control parameter for how incidence falls over time). Note, current projections represent an optimistic scenario because of the high value for d. If R0=1·75 and d=0·006125, a final epidemic size of greater than 8 million cases is projected.
www.thelancet.com/infection Published online October 24, 2014 http://dx.doi.org/10.1016/S1473-3099(14)70851-5
1
Comment
simple mathematics: if R0 in this region is around 2·5, as Lewnard and colleagues estimate, incidence in every successive epidemic generation will increase by 150%. If R0 could be pushed to less than one, incident case counts would begin to drop, but because incident cases are a function of prevalent cases, making this decrease happen earlier in the epidemic results in striking reductions in final epidemic size (figure). For example, if R0 is reduced to 0·9 at a time when there are 1000 incident cases per generation, case counts in subsequent generations will be 900, 810, 720, and so on. If intervention is delayed until there are 10 000 cases per generation and R0 is cut to 0·9, subsequent generations will have 9000, 8100, 7200 cases, and so on. Elevated case counts also increase the risk of spread to as yet unaffected areas, sparking new outbreaks. Researchers have asserted that the epidemic is proceeding in virus time, with a response on bureaucrat time.7 From a global perspective, controlling the Ebola epidemic in west Africa is not only a humanitarian duty but also a matter of crude self-interest. The report by Lewnard and colleagues shows that intervention will only be meaningful if it is timely, and so far it has not been.
2
*David Fisman, Ashleigh R Tuite Dalla Lana School of Public Health, University of Toronto, Toronto, ON, Canada M5T 3M7 david.fi[email protected] We declare no competing interests. 1 2
3
4
5
6
7
Farrar JJ, Piot P. The Ebola emergency: immediate action, ongoing strategy. N Engl J Med 2014; 371: 1545–46. Doucleff M. No, seriously, how contagious is Ebola? Oct 2, 2014. http:// www.npr.org/blogs/health/2014/10/02/352983774/no-seriously-howcontagious-is-ebola (accessed Oct 19, 2014). Lewnard JA, Ndeffo Mbah ML, Alfaro-Murillo JA, et al. Dynamics and control of Ebola virus transmission in Montserrado, Liberia: a mathematical modelling analysis. Lancet Infect Dis 2014; published online Oct 24. http:// dx.doi.org/10.1016/S1473-3099(14)70995-8. Liberian Ministry of Health and Social Welfare. Situation reports. Oct 11, 2014. http://www.liberianhealthresearch.com/reports.html (accessed Oct 20, 2014). WHO. WHO: Ebola response roadmap situation report. Oct 15, 2014. http:// apps.who.int/iris/bitstream/10665/136508/1/roadmapsitrep15Oct2014. pdf?ua=1 (accessed Oct 20, 2014). Fisman DN, Khoo E, Tuite AR. Early epidemic dynamics of the west African 2014 Ebola outbreak: estimates derived with a simple two-parameter model. PLoS Curr 2014; published online Sept 8. http://dx.doi.org/10.1371/ currents.outbreaks.89c0d3783f36958d96ebbae97348d571. Achenbach J, Sun LH, Dennis B. The ominous math of the Ebola epidemic. Oct 9, 2014. http://www.washingtonpost.com/national/health-science/ the-ominous-math-of-the-ebola-epidemic/2014/10/09/3cad9e76-4fb211e4-8c24-487e92bc997b_story.html (accessed Oct 20, 2014).
www.thelancet.com/infection Published online October 24, 2014 http://dx.doi.org/10.1016/S1473-3099(14)70851-5
Ebola: no time to waste
18 000
Current projections R=0·9, January, 2015 R=0·9, November, 2014
Lancet Infect Dis 2014 Published Online October 24, 2014 http://dx.doi.org/10.1016/ S1473-3099(14)70851-5 See Online/Articles http://dx.doi.org/10.1016/ S1473-3099(14)70995-8
300 000
16 000 250 000 14 000 200 000
12 000 10 000
150 000 8000 100 000
6000
Cumulative incidence
4000 50 000 2000 0
31 ,2
01 6 Au g1 8, 20 16
0
Jan
The 2014 Ebola epidemic, already devastating to those countries most affected, threatens to evolve into a health and humanitarian catastrophe of historic scope.1 As infectious disease epidemiologists, we note with sadness that the epidemic has brought the notion of exponential growth into the popular sphere, with media sources buzzing with talk of basic reproductive numbers (R0).2 Indeed, the growth of this epidemic fits so well with mathematical epidemiological ideas that it seems torn from the pages of a textbook. And thus, even as the current Ebola epidemic wastes lives, devastates economies, and causes widespread fear, it follows a seemingly well behaved epidemiological process, readily understood through the use of mathematical modelling. In The Lancet Infectious Diseases, Joseph Lewnard and colleagues3 developed a mathematical model to predict the transmission of Ebola virus disease (EVD) in Montserrado County, Liberia, up to Dec 15, 2014. This region, home to Monrovia, Liberia’s capital, has been severely affected by EVD, with more than 1600 cases and 1000 deaths reported as of Oct 14, 2014.4 The authors used their model to assess the effectiveness of three interventions to control the Ebola outbreak: allocation of additional beds by construction of EVD treatment centres; acceleration of case ascertainment; and distribution of protective kits for home care for all newly ascertained cases. With epidemiological data, Lewnard and colleagues estimated the R0 of EVD to be 2·49 (95% CI 2·38–2·60). With their mathematical model, they predicted that expansion of the capacity of EVD treatment centres alone is not nearly as effective as coupling it with more rapid case ascertainment, because ascertainment reduces the infectiousness of cases. For example, providing 2400 beds over a period of 2 weeks, while concurrently accelerating case ascertainment five-fold, was projected to avert 62 220 (53 556–70 654) EVD cases by Dec 15, 2014. Of note, these bed numbers for EVD treatment centres are optimistic: the bestcase scenario assumes up to 4800 beds available by Dec 15, 2014, but as of Oct 15, 2014, Liberia reports that only six of 28 planned EVD treatment centres are
Incident cases (per 15 day generation)
William Shakespeare, King Richard II
operational, providing 620 of 2930 planned beds.5 Provision of protective home care kits became an important strategy in the model when beds at EVD treatment centres were not available. For example, distribution of kits to households of ascertained cases for whom no beds are available is projected to avert between 4497 (95% CI –5153 to 13 524) and 30 557 (22 535 to 38 663) cases, by Dec 15, 2014, corresponding to intervention efficacy ranging from 10% to 50%. Perhaps the most striking result of this study is the importance of timing of intervention rollout on projected disease dynamics. Lewnard and colleagues show that if all three interventions were initiated 2 weeks earlier than in the base case (ie, Oct 15, 2014, rather than Oct 31, 2014), up to 137 432 (129 736–145 874) cases of EVD could have been averted, compared with up to 97 940 (90 096–105 606) cases. Of course, by the time this report is published, Oct 15, 2014 will be a historical date, but the key takehome message for readers is this: we have no time to waste. The urgency of timely intervention in the Ebola epidemic cannot be overstated. The reason is one of
No v2 2, 20 13 Ju ne 10 ,2 01 4 De c2 7, 20 14 Ju ly 15 ,2 01 5
“I wasted time, and now doth time waste me”
Figure: Projected course of the 2014 Ebola epidemic using the IDEA model The projection is based on global case count data to Oct 18, 2014.6 Dark green curves represent projections under the current level of control (solid curve represents incidence, dashed curve represents cumulative incidence). Corresponding red and blue curves represent projections in the face of a decline in reproductive number after control (R) to 0·9 by January, 2015, or November, 2014, respectively. Model parameters: R0=1·858, d=0·009954 (d is a control parameter for how incidence falls over time). Note, current projections represent an optimistic scenario because of the high value for d. If R0=1·75 and d=0·006125, a final epidemic size of greater than 8 million cases is projected.
www.thelancet.com/infection Published online October 24, 2014 http://dx.doi.org/10.1016/S1473-3099(14)70851-5
1
Comment
simple mathematics: if R0 in this region is around 2·5, as Lewnard and colleagues estimate, incidence in every successive epidemic generation will increase by 150%. If R0 could be pushed to less than one, incident case counts would begin to drop, but because incident cases are a function of prevalent cases, making this decrease happen earlier in the epidemic results in striking reductions in final epidemic size (figure). For example, if R0 is reduced to 0·9 at a time when there are 1000 incident cases per generation, case counts in subsequent generations will be 900, 810, 720, and so on. If intervention is delayed until there are 10 000 cases per generation and R0 is cut to 0·9, subsequent generations will have 9000, 8100, 7200 cases, and so on. Elevated case counts also increase the risk of spread to as yet unaffected areas, sparking new outbreaks. Researchers have asserted that the epidemic is proceeding in virus time, with a response on bureaucrat time.7 From a global perspective, controlling the Ebola epidemic in west Africa is not only a humanitarian duty but also a matter of crude self-interest. The report by Lewnard and colleagues shows that intervention will only be meaningful if it is timely, and so far it has not been.
2
*David Fisman, Ashleigh R Tuite Dalla Lana School of Public Health, University of Toronto, Toronto, ON, Canada M5T 3M7 david.fi[email protected] We declare no competing interests. 1 2
3
4
5
6
7
Farrar JJ, Piot P. The Ebola emergency: immediate action, ongoing strategy. N Engl J Med 2014; 371: 1545–46. Doucleff M. No, seriously, how contagious is Ebola? Oct 2, 2014. http:// www.npr.org/blogs/health/2014/10/02/352983774/no-seriously-howcontagious-is-ebola (accessed Oct 19, 2014). Lewnard JA, Ndeffo Mbah ML, Alfaro-Murillo JA, et al. Dynamics and control of Ebola virus transmission in Montserrado, Liberia: a mathematical modelling analysis. Lancet Infect Dis 2014; published online Oct 24. http:// dx.doi.org/10.1016/S1473-3099(14)70995-8. Liberian Ministry of Health and Social Welfare. Situation reports. Oct 11, 2014. http://www.liberianhealthresearch.com/reports.html (accessed Oct 20, 2014). WHO. WHO: Ebola response roadmap situation report. Oct 15, 2014. http:// apps.who.int/iris/bitstream/10665/136508/1/roadmapsitrep15Oct2014. pdf?ua=1 (accessed Oct 20, 2014). Fisman DN, Khoo E, Tuite AR. Early epidemic dynamics of the west African 2014 Ebola outbreak: estimates derived with a simple two-parameter model. PLoS Curr 2014; published online Sept 8. http://dx.doi.org/10.1371/ currents.outbreaks.89c0d3783f36958d96ebbae97348d571. Achenbach J, Sun LH, Dennis B. The ominous math of the Ebola epidemic. Oct 9, 2014. http://www.washingtonpost.com/national/health-science/ the-ominous-math-of-the-ebola-epidemic/2014/10/09/3cad9e76-4fb211e4-8c24-487e92bc997b_story.html (accessed Oct 20, 2014).
www.thelancet.com/infection Published online October 24, 2014 http://dx.doi.org/10.1016/S1473-3099(14)70851-5
