Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (3): 851-866.

Previous Articles     Next Articles

Dynamics of an Anthrax Epidemiological Model with Time Delay and Seasonality

Tailei Zhang1,Junli Liu2,*(),Mengjie Han2   

  1. 1 School of Science, Chang'an University, Xi'an 710064
    2 School of Science, Xi'an Polytechnic University, Xi'an 710048
  • Received:2021-08-23 Online:2022-06-26 Published:2022-05-09
  • Contact: Junli Liu
  • Supported by:
    the NSFC(11801431);the Natural Science Basic Research Plan in Shaanxi Province(2021JM-445);the Natural Science Basic Research Plan in Shaanxi Province(2022JM-023)


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

CLC Number: 

  • O175.1