The Research Of Several Kinds Of Epidemic Model

This paper consists of three parts:Firstly, this paper discusses an epidemic model of a predator-prey system with epidemic.The conditions and threshold to the existence of various equilibriums are established. By using the characteristic root method, Hurwitz criterion and Lyapunov-La Salle invariant set theorem, we obtained the stability of various equilibriums and optimal harvesting based on the global stability of the positive equilibrium.Secondly, a stochastic predator-prey system with Beddington-De Angelis functional response and epidemic in prey is proposed and investigated. First, we show that there is a unique global positive solution to the model for any positive initial value. Second, we show the conditions and threshold to the permanence and extinct. At last, we discuss the gradual property to the solution of the stochastic model.Thirdly, an epidemic model of a stochastic and non-autonomous predator-prey system with epidemic and media report is considered. First, we show that there is a unique global positive solution to the model for any positive initial value and it is random ultimately bounded. Second, we discuss the su?cient condition about extinction、the non-average continued survival and the weak persistence in the mean of the population. At the same time, We also get the threshold of prey to the weak persistence in the mean and extinct.