Abstract:

In this paper, we developed a time-delayed epidemiological model to describe the anthrax transmission, which incorporates seasonality and the incubation period of the animal population. The basic reproduction number $R_{0}$ can be obtained. It is shown that the threshold dynamics is completely determined by the basic reproduction number. If $R_{0}<1$, the disease-free periodic solution is globally attractive and the disease will die out; if $R_{0} >1$, then there exists at least one positive periodic solution and the disease persists. We further investigate the corresponding autonomous system, the global stability of the disease-free equilibrium and the positive equilibrium is established in terms of $[R_0]$. Numerical simulations are carried out to investigate the sensitivity of $R_0$ about the parameters, the effects of vaccination and carcass disposal on controlling the spread of anthrax is also analyzed.

Key words: Anthrax model, Time delay, Basic reproduction number, Seasonality, Threshold dynamics