Qualitative Analysis Of Two Stochastic SIRI Models

Infectious diseases can spread between people and animals,its transmission speed is fast and it can lasting for a long time.It will not only destroy the health,but also cause losses to the national economy and it is the disaster of all mankind.Through mathematical models to analysis the spread of infectious diseases can help us to predict the trend of the disease,implement scientific control measures in advance and reduce losses.Environmental changes have an impact on the spread of infectious diseases,so thinking the impact of the stochastic environment can better simulate the spread of infectious diseases.Based on the above two factors,this paper mainly studies two types of stochastic SIRI models.The first chapter explains the necessity of studying infectious diseases by introducing the harmfulness of infectious diseases and its spreading rules.Then we introduce the research dynamics of infectious diseases and the influence of stochastic environmental factors on infectious diseases.Finally,we explain the research objects,research contents and research methods of stochastic infectious diseases model.The second chapter studies a stochastic SIRI model with L(?)vy jump and media reportFirstly,the existence and uniqueness of the global positive solution of the model are obtained by constructing an appropriate Lyapunov function.Then we construct an appropriate Lyapunov function to obtain the solution’s asymptotic property that arounds the corresponding deterministic model’s disease-free equilibrium point and endemic equilibrium point.Finally,the theoretical results are verified through the numerical simulation.The third chapter studies a stochastic SIRI model with different incidence and two-parameter perturbationsFirstly,the existence and uniqueness of the global positive solution of the model are obtained by constructing an appropriate Lyapunov function.Then by using Lyapunov function,Gronwall inequality and strong number theorem,we prove the sufficient conditions for the extinction and average persistence of infectious diseases.Finally,the theoretical results are verified through the numerical simulation.The forth chapter summarizes the content of the previous two chapters and gives directions for future research.