Dynamical Analysis Of Multiple Populations Eco-epidemiological Model With Delay

Eco-epidemical model is an important theme of epidemic models.The research of the infectious diseases only considers the spread of disease in single species at now,but species is not isolated exist in nature,who compete with each other or are captured by other species due to competition for food,space,resources,etc.We need find the corresponding control measures to reduce the spread of disease in the ecosystem.Thus,we will constructer ecoepidemiology models and study their stabilities,bifurcations and optimal controls.In Chapter 2,we study a predator-prey system with harvesting prey and disease prey species.In the absence of time delay,by constructing Lyapunov functions,sufficient conditions for the global asymptotic stability of the equilibrium are obtained.In the presence of time delay,the existence of Hopf bifurcation is given.By using the normal form theory and center manifold theorem,the properties of Hopf bifurcation are given.Furthermore,an optimal harvesting policy is investigated by Pontryagin's Maximum Principle.Numerical simulations are performed to support our analysis results.In Chapter 3,we propose a food chain model with time delay dependent coefficient of infected prey capable reproduce.The sufficient conditions for the asymptotic stability of equilibrium point and the existence of Hopf bifurcation are given.By using the normal form theory and center manifold theorem,the direction of Hopf bifurcation,the stability and expression of Hopf bifurcation periodic solution are obtained.The results of theoretical analysis are verified by numerical simulation.In Chapter 4,we investigate a food chain system with two predators infected by an infectious disease.Through analyzing the thresholds of the model,the stability of all equilibria are given.By using the center manifold theory,the conditions of backward and forward bifurcation are obtained.We have also study that such system exhibits a Hopf bifurcation in the neighbourhood of the endemic equilibrium.Furthermore,the optimal control of the disease is discussed by the Pontryagin's Maximum Principle.Numerical simulations are given to support the conclusion.