Researches On An Eco-Epidemiological Model With Patch Structure And Transport-related Infection

Based on researches of travel-related infection of single population among patches,in chapter 2,the epidemic dynamics and population dynamics are combined to propose an Eco-Epidemiological model with patch structure and transport-related infection,which only the predator population is infected.In addition,suppose that every population will inevitably be affected by environmental noise in natural world and,white noise is incorporated,and a stochastic Eco-Epidemiological model is established in chapter 3.For the deterministic Eco-Epidemiological model,this paper firstly proves that the solutions are positively definite and uniformly bounded under initial conditions,and the permanence of the system is obtained.Again,by analyzing the equilibrium points of the proposed model,the existence conditions of all equilibria,the local asymptotic stability conditions and the global asymptotic stability conditions of boundary equilibrium E1 and EI0 are obtained.Finally,this paper analyzes the conditions for the occurrence of Hopf bifurication at the inner equilibrium.The numerical simulations are conducted to test the analysis results and explain the influence of infection coefficient during the transportion and travel rate(diffusion rate)on disease.For the stochastic Eco-Epidemiological model,by constructing appropriate Lyapunov functions,the existence and uniqueness of the global positive solution of the proposed model firstly is proved.And also,it is shown that the model is ultimately bounded in mean,stochastically ultimately bounded and the average in time of the second moment of solution is bounded.Secondly,it is proved that the solution of the stochastic model will fluctuate around the equilibria of the deterministic model with the same parameters when the white noise intensity is relatively small.However,large enough white noise intensity may lead the total predator population or disease in the predator to be extinct in scenarios where the deterministic system is persistent.Finally,all analysis results are illustrated by numerical simulation.