The Stability Of A Predator-Prey Model With Disease

This paper discusses predator-prey model with infectious disease, at the same time, the time delay and ratio-dependence function considered in the model. The stability of the model is that the paper mainly researches.In Chapter 1, The model established of this paper is carried out, thought know-ing about the background of the biomathematics model and a few predator-prey infectious disease models studied at home and abroad. Chapter 2 shows the model: Considering the boundedness of solutions of the model, the existence and the local asymptotically stability of each of the equilibria (predator-extinction equilibrium, disease-free equilibrium and the coexistence equilibrium) of the model.First, according to the theory of differential inequalities, the boundedness of solutions of the model has been proposed. Secondly, the sufficient conditions of the existence of three equilibria are concluded by analying the existence of three equilibria. End, we can arrived at corresponding characteristic equations at the different equilibria on the model linearization. Then, the local stability of each of the equilibria is established, in the meantime, we draw the sufficient conditions of the local asymptotically stability of each of three equilibria. Numerical simulations are carried out to support the theoretical analysis.Chapter 3, Similarly, considering the model (*). By using the theory of differ-ential equation, the sufficient conditions of global stability of predator-extinction equilibrium are obtained. Then, according to the iterative method, several iterative sequences are constructed. Hence, we can reach the sufficient conditions of global stability of disease-free equilibrium.