Mathematical analysis and simulations of models for rabies epidemic among African wild dogs (Lycaon pictus)

Abstract

Simplified models representing rabies epidemic are presented to better understand the epidemiological dynamics of the disease. We extensively study the transmission and progression dynamics of rabies in African wild dogs, Lycaon pictus, by adapting a stan-dard sei model to include both the asymptomatic and symptomatic stages to simulate the time-delay. Furthermore, we investigate the contribution of other rabies hosts in the environment (e.g, stray dogs) have on the transmission dynamics. The study is based on the assumption that there are no vaccination programmes introduced, hence, we consider culling as a possible control strategy to reduce the rabid population or the uncontrollable spread of the disease to a level below the threshold. The threshold quantity, the basic reproduction number, which in this case is the expected number of new infectious dogs in a perfectly susceptible population produced by a single infected dog is used to give a quantitative discussion on the control of rabies. We present the mathematical analysis of the proposed continuous and discrete models. Numerical simulations are provided to support theoretical results.