Two Types Of Ecosystem Dynamics System Of Infectious Diseases Model Analysis And Research

As we all know, species is not isolated exist in nature. They are always competing with others for food and partnership or preying. Eco-epidemiology dynamic model is mainly studied of interact populations with influence by combining population ecology and infectious disease dynamics. It is playing a very important reference value and guidance for controlling disease spread between populations and treatment of disease or preventing disease. In this paper, we perform researches of two models of eco-epidemiology in predator-prey system, which include: epidemics of a strengthened in predator-prey model with bilinear incidence and disease in predator, epidemic of two delays in predator-prey model with bilinear incidence and disease in prey. We obtain the following main results.1. When disease that is infected bilinear is spread among the predator population, we set up epidemics of a strengthened in predator-prey system with bilinear incidence and disease in predator. The system boundary of solutions of the proposed system and the existence of equilibrium are studied, and the boundary of the local asymptotic stability of the equilibrium point, and the sufficient conditions for meeting locally asymptotic stability of the equilibrium are obtained. Furthermore, the sufficient conditions of the extinction of infective predator population, predator population of disease extinction (disease disappear) and three kinds of population stability coexistence (epidemic persistence) are obtained from analyzing the global stability of the equilibrium. Test the correctness of the theorem and the effect of the attack rate on the stability of the system is analyzed by numerical simulation.2. When disease that is infected bilinear is spread among the prey population, we set up epidemics of two delays in predator-prey system with bilinear incidence and disease in prey. The system boundary of solutions of the proposed system and the existence of equilibrium are studied, and the boundary of the local asymptotic stability of the equilibrium point, and the sufficient conditions for meeting locally asymptotic stability of the equilibrium are obtained. Furthermore, the sufficient conditions of the global stability of the positive equilibrium and three kinds of population stability coexistence (epidemic persistence) are obtained with no delay. Test the correctness of the theorem and the effect of the attack rate and delay on the stability of the system is analyzed by numerical simulation.