Stability analysis of interaction model between anthrax and rabies

Abstract

In order to study the interaction between zebra anthrax and scavenger jackals rabies, a deterministic infectious disease model was established. By using the basic theorem of differential equation, the nonnegativity and boundedness of the solution of the model were proved, the sufficient conditions for the existence of the equilibria given, three kinds of reproduction numbers of the model defined, and the stability of the equilibria was analyzed by linearization method and numerical simulation method. The effects of model parameters on the number of infected carcasses and infected jackals in equilibrium were studied by numerical simulation, and the interaction between anthrax and rabies was studied. The results show that anthrax and rabies can aggravate the transmission of each other.

Keywords

• anthrax
• rabies
• basic reproduction number
• stability
• hopf bifurcation