How Valid Are Assumptions About Re-emerging Smallpox? A Systematic Review of Parameters Used in Smallpox Mathematical Models.

Background: Globally eradicated in 1980, smallpox is listed as a category A bioterrorism agent. If smallpox were to re-emerge, it may be due to an act of bioterrorism or a laboratory accident, and the impact is likely to be severe. Preparedness against smallpox is subject to more uncertainty than other infectious diseases because it is eradicated, there is uncertainty about population immunity, and the current global health workforce has no practical experience or living memory of smallpox. In the event of re-emergence of smallpox, mathematical modeling plays a crucial role in improving the evidence base to inform preparedness, mitigation, and response activities. However, the predictions of mathematical models about outbreak magnitude and impact depend critically on the assumptions and disease parameters used. We aimed to identify modeling studies that would be applicable to re-emerging smallpox and to evaluate consistency and the certainty of the evidence published about the key parameters used.

Methods: We conducted a systematic review using PRISMA criteria, of assumptions used in modeling studies on duration of latent, prodromal, and infectious period, as well as the choice of the basic reproduction number (R0) for re-emerging smallpox. We performed a literature search using PubMED, Scopus, Web of Science, and EMBASE and included peer-reviewed articles that focused on smallpox models, stated at least three of the aforementioned parameters and published in English.

Findings: A total of 42 studies were selected for inclusion. There was general agreement on the duration of latent and prodromal periods, being 11-12 d (88%) and 3 d (59%), respectively. The duration of the infectious period varied from 4 to 20 d. Most models assumed 16 d (19%), 12 d (16.7%), and 8.6 d (12%) of infectiousness. In 25/34 studies, R0 ranged between 3 and 5, generally lower than the R0 calculated from past outbreaks.

Discussion: Models of smallpox re-emergence also tend to use the same limited available historical data sources but assume a wide range of different estimates for key parameters. Models use very optimistic assumptions of decreased population immunity, despite high uncertainty about duration and magnitude of post-vaccination immunity. This review reveals a paradox. A substantial proportion of the modern population is unvaccinated, never exposed to boosting from wild-type smallpox, or immunocompromised; furthermore, vaccine-induced immunity wanes over time. Failure to consider these factors in a model will lead to underestimating the true impact of a re-emergent smallpox epidemic in the contemporary population.