Groupe d’études et de recherche en analyse des décisions

A Bayesian SEIR approach to modeling smallpox epidemics

Vanja Dukic

Much of the recent US public-policy debate regarding smallpox vaccination has focused on mass versus trace vaccination strategies; namely, whether the public can be better protected by vaccination of the entire population or of only those who have been in contact with infected individuals. Much of the previous work on smallpox policy has generally employed relatively complex deterministic epidemics models, with many biological parameters fixed, and focusing mostly on a single point estimate of the disease reproductive rate (the number of newly infected individuals arising from a single infected individual). In this talk we present a Bayesian susceptible-exposed-infected-recovered (SEIR) model and apply it to analyze a set of eight smallpox epidemics in Southwest Native American mission communities during 1780-1781. Of interest is the posterior distribution of the basic reproductive rate R0 (a parameter which in a given society describes the expected number of secondary infections resulting from a single infected individual during his/her lifetime), after taking into account the uncertainty of all other parameters in the model, as well as population and geographical heterogeneity. We then present a comparison of the two vaccination strategies based on the posterior predictive distribution of the fatalities under several prior distribution choices.