Research On Two Types Of Stochastic Eco-epidemiology Dynamical Models

This paper mainly investigates the dynamic behavior of two kinds of infectious diseases. Firstly, we investigate a stochastic predator-prey model with disease in prey. By using stochastic differential equation theory, we study the long time behavior of positive solutions of the stochastic system. Then, by using evolutionary dynamics theory, we study the adaptive evolutionary behavior of the population under environmental noise, and obtain the conditions for the evolutionary branch and evolutionary stability of the variation population. Then we use the numerical simulation to verify the theoretical results. Secondly,we study a stochastic eco-epidemic model with Beddington-DeAngelis functional response. Based on the theory of stochastic differential equation and some important inequalities, we study the long time behavior of the solution of the system, and obtain the conditions of the persistence in mean and extinction of the system. Then we use the Matlab numerical simulation to verify the theoretical results. Our theoretical results provide a theoretical basis for the protection of species diversity.In Chapter 1, we first introduce the research background of the subject, and then introduce the theory of stochastic differential equations and evolutionary dynamics.In Chapter 2, we propose a stochastic predator-infected prey model,by using Lyapunov method and stochastic differential equations theory,we obtain the long time behavior and ergodicity of the solutions. Then,by using the adaptive evolutionary dynamics method, we obtain the fitness function with stochastic noise, and study the evolutionary branch and evolutionary stability of pathogenic bacteria in infected prey. Finally,we use the numerical simulation to verify the theoretical results. The biological significance of the theoretical results shows that large random interference will lead to the evolution of the virus in the direction of toxicity reduction, which provides a theoretical basis for the control of the disease.In Chapter 3, we first propose a stochastic eco-epidemic model with Beddington-DeAngelis functional response. By using Lyapunov method and stochastic differential equations theory, we obtain the long time behavior and ergodicity of the solutions. Then, by using the stochastic differential equation theory and inequality method, we obtain the conditions of the persistence in mean and extinction of the system.Finally, we use the numerical simulation to verify the theoretical results.The results show that the external environment disturbance may have a certain effect on the stability of the biological system: if the disturbance in the environment is small enough, the stability of the population will not be destroyed; if large disturbances occur in the environment, it may lead to the extinction of species.In Chapter 4, we make a summary of the full paper, and make a forward-looking vision of the future research work .