Dynamics Analysis Of Anthrax Model In Animal Population

In this paper,according to the characteristics of anthrax diseas transmission,a reasonable and operable anthrax disease model is established,and its dynamics analysis is of great significance for the control of anthrax disease.Firstly,the anthrax disease model with incubation period and Logistic growth has been studied.We have calculated the reproductive numberR₀.If0R?27?,1there exists only the disease-free equilibrium which is globally asymptotically stable by the Lyapunov function and theorem of Lasalle invariant set,which meant that anthrax disease would eventually disappear;if₀R?29?,1 there was a unique endemic equilibrium in the system.It was proved by Routh-Hurwitz criterion that the equilibrium point was locally asymptotically stable when the corresponding conditions were satisfied.Numerical simulation shows that the system has Hopf bifurcation under certain conditions,and the outbreak of anthrax is periodic.Secondly,we extend the traditional anthrax disease model and consider the factors that mosquitoes such as flies and lice transmit anthrax spores through biting,thus establishing a kind of anthrax disease model with vector population.According to the definition of epidemic transmission,we calculate the basic reproduction number of anthrax epidemic conditions.When0R?27?,1we find that the system was globally asymptotically stable at that time.If0R?29?,1the Routh-Hurwitz criterion proves that the endemic equilibrium is locally asymptotically stable when certain conditions are satisfied.