Dynamics Analysis Of Two Eco-epidemiological Models With Disease In The Predator

The health of human is under the dire threat of infectious diseases.How to control disease spread is an important problem which should be paid much attention to. In recent years, there is a great development of epidemic dynamics,which help us to understand how to reduce disease transmission.A species does not exist alone in the nature world,so disease can spread between different species.The study of interact populations with epi-demic is termed as eco-epidemiology which is a combination of population dynamics and epidemic dynamics. It plays a very important role for preventing and controlling disease spread.An eco-epidemiological model with disease and vertical infection in the predator and a strengthen type eco-epidemiological model with disease in the predator are analyzed in this paper.We obtain the following main results.1.A strengthen type predator-prey model of predator with disease and standard inci-dence is formulated and analyzed.The boundness of solutions of the proposed system and the existence of equilibrium are studied, and the sufficient conditions of locally asymp-totically stable of the equilibrium are obtained by the Routh-Hurwitz criterion.Further-more,we analyze the global stability of the equilibrium by using Lyapunov functions. The condition of t the permanence of system is obtained.2.The effect of the attack rate on the stability of the system is analyzed by numerical simulation.3.A predator-prey model of predator with disease and vertical transmission is formu-lated and analyzed.The boundness of solutions of the proposed system and the existence of equilibrium are studied, and the sufficient conditions of locally asymptotically stable of the equilibrium are obtained by the Routh-Hurwitz criterion. The conditions of the extinction of prey,the extinction of disease and the disease persistence are obtained by analyzing the global stability of the equilibrium by using Lyapunov functions.The above show that, the attack rate of infected predator and vertical transmission can make it easier for the disease spread between populations.