Decoupling environmental effects and host population dynamics for anthrax, a classic reservoir-driven disease

Abstract

Quantitative models describing environmentally-mediated disease transmission rarely focus on the independent contribution of recruitment and the environment on the force of infection driving outbreaks. In this study we attempt to investigate the interaction between external factors and host’s population dynamics in determining the outbreaks of some indirectly transmitted diseases. We first built deterministic and stochastic compartmental models based on anthrax which were parameterized using information from literature and complemented with field observations. Our force of infection function was derived modeling the number of successful transmission encounters as a pure birth process that depends on the pathogen’s dispersion effort. After accounting for individual heterogeneity in pathogen’s dispersion effort, we allowed the force of infection to vary seasonally according to external factors recreating a scenario in which disease transmission increases in response to an environmental variable. Using simulations we demonstrate that anthrax disease dynamics in mid-latitude grasslands is decoupled from hosts population dynamics. When seasonal forcing was ignored, outbreaks matched hosts reproductive events, a scenario that is not realistic in nature. Instead, when allowing the force of infection to vary seasonally, outbreaks were only present in years were environmental variables were appropriate for the outbreaks to develop. We used the stochastic formulation of the force of infection to derive R ₀ under scenarios with different assumptions. The derivation of R ₀ allowed us to conclude that during epizootic years, pathogen contribution to disease persistence is nearly independent of dispersion. In endemic years, only pathogens with high dispersion significantly prevent disease extinction. Finally, we used our model in a maximum likelihood framework to estimate the parameters that determined a significant anthrax outbreak in Montana in 2008. Our study highlights the importance of the environment in determining anthrax outbreak intensity and could be useful to predict future events that could result in significant wildlife and domestic livestock losses.