Population-level proportions of individuals that fall at different points in the spectrum [of disease severity], from asymptomatic infection to severe disease, are often difficult to observe, but estimating these quantities can provide information about the nature and severity of the disease in a particular population. Logistic and multinomial regression techniques are often applied to infectious disease modeling of large populations and are suited to identifying variables associated with a particular disease or disease state. However, they are less appropriate for estimating infection state prevalence over time because they do not naturally accommodate known disease dynamics like duration of time an individual is infectious, heterogeneity in the risk of acquiring infection, and patterns of seasonality. We propose a Bayesian compartmental model to estimate latent infection state prevalence over time that easily incorporates known disease dynamics. We demonstrate how and why a stochastic compartmental model is a better approach for determining infection state proportions than multinomial regression is by using a novel method for estimating Bayes factors for models with high-dimensional parameter spaces. We provide an example using visceral leishmaniasis in Brazil and present an empirically-adjusted reproductive number for the infection.
Keywords: Bayes factor; SIR; empirically-adjusted reproductive number; multinomial; seasonality; visceral leishmaniasis.