Analysis Of Awareness Program On Epidemic Model Influenced By Nonlinearity And Noise

Establishing mathematical models is an important method to study the spread and control of infectious diseases.With the rapid development of science technology and electronic media,people have many ways to receive information,including the information of infectious diseases.It makes us consider the influence of disease information consciousness on susceptible population when we study infectious diseases and establish corresponding mathematical models.Generally speaking,environmental noise has a certain impact on biological systems.Therefore,on the basis of previous research results,this paper proposes a stochastic epidemic model affected by disease information,improves the model more rationally.And then the SIQS model with Ornstein-Uhlenbeck process is studied.By using the theory of differential equation,we analyzed the dynamics of the models.In the second chapter,we study a stochastic epidemic model with non-linear incidence affected by disease information,and analyze the impact of media coverage and environmental noise on the model.The results are proved by theories of differential equation.We know that when the basic reproduction number R0<1,the disease-free equilibrium point E0 of the deterministic model is globally asymptotically stable.When the basic reproduction number R0>1,the endemic equilibrium point E of the deterministic model is also stable.By using the theories of stochastic differential equation,the existence of positive global solution about the stochastic system is proved.When the stochastic basic reproduction number R0s<1,the noise intensity is large enough,the disease will eventually tend to zero exponentially.Finally,the numerical simulations validates the correctness of the theoretical analysis.That is to say,Media coverage and random noise have an important impact on the dynamics of epidemic models.In the third chapter,the stochastic SIQS model with Ornstein-Uhlenbeck process is analyzed.Firstly,by constructing Liapunov function and using the formula of It(?),the existence and uniqueness of global positive solutions for stochastic model are proved.Secondly,the impact of stochastic noise is analyzed by using stochastic differential equation theory.It is concluded that when R0s is less than 1,the disease will be extinct with probability 1.Generally,human beings can establish the mathematical models of diseases which are affected by disease information and random noise to analyze the epidemic in a realistic way,and also promote us to have a deeper understanding of the epidemic models.