Asymptotic Behavior Of A Stochastic SEIR Epidemic Model With Nonlinear Incidence Rate

The use of mathematical models to characterize the mechanism of disease transmission is of great significance for the study of infectious diseases.Many scholars have studied the transmission mechanism of infectious diseases by establishing mathematical models,thus Making predictions and judgments of communication.Factors such as the environment can affect the spread of disease,There will be a delay when the disease spread between people,that will make our research more realistic.Meaning,then based on the deterministic model,a stochastic SEIR model is established,and a stochastic SEIR model with time delays.In the third chapter,we study a class of stochastic SEIR epidemic models with nonlinear incidence.Firstly,the system is proved to have a unique global positive solution.Then,by constructing some appropriate Lyapunov functions and the It(?) formula,we analyze the asymptotic behavior of the disease-free equilibrium and endemic equilibrium.Finally,the asymptotic behavior of the stochastic system solution is further analyzed by numerical simulation and the conclusions of this paper are given.In the fourth chapter,we study a stochastic delayed SEIR epidemic model with nonlinear incidence.Firstly,We proved that the system has a unique global positive solution.Then,by constructing some appropriate Lyapunov functions and the It(?) formula,we analyze the asymptotic behavior of the disease-free equilibrium and endemic equilibrium.Finally,the asymptotic behavior of the stochastic system solution is further analyzed by numerical simulation and the conclusions of this paper are given.