Dynamic Behaviour Of A Stochastic Epidemic Model With Media Coverage And Partial Immunity

Epidemic seriously affect human health and social well-being.Mathematical model is one of the most important tools to explore the spread,control and eliminate of epidemic.This paper consider on the effects of environmental white noise on epidemic and establishes of the corresponding stochastic epidemic modes.This paper consists of three parts,the specific content is as follows.In chapter 1,we introduce the biological background and significance of the infectious disease model,and then give the stochastic epidemic model to be studied in this paper and the relevant knowledge for needed.In chapter 2,we discuss a class of stochastic SIR epidemic model with media coverage.Firstly,we prove that the stochastic model has a unique global positive solution.Then,we study the sufficient conditions of disease extinction and the asymptotic behavior of the solution of the stochastic model at the endemic equilibrium point of deterministic system.Furthermore,we obtain the conditions that the stochastic model has stable distribution and ergodicity.In addition,we give the numerical simulation to support the above conclusions.In chapter 3,firstly,we assume that the intensity of the stochastic perturbation is proportional to the system variable and establish a stochastic SIRS epidemic model with standard incidence and partial immunity,which prove that the existence and uniqueness of global positive solutions of stochastic model.Secondly,we give the sufficient condition that the stochastic model has stable distribution and the extinction of the disease.In addition,we assume that impact of stochastic perturbation on the contact rate of deterministic systems and establish a stochastic SIRS epidemic model with standard incidence and partial immunity under parameter disturbance.Then,we prove that the existence and uniqueness of the global positive solution of the stochastic model.Secondly,we establish the sufficient conditions for the extinction and persistence in mean of diseases.Finally,we verify the above the results by numerical simulation.