Complexity Analysis Of A Class Of Stochastic Epidemic Models In Network

Infectious diseases have always been a great threat to human health.And infectious diseases are still the leading killer of the world’s population today.Therefore,it is particularly important to study the pathogenesis,transmission rules and control methods of infectious diseases.At present,the dynamics of infectious diseases is an important method of theoretical research on infectious diseases.Through the pathogenesis of infectious diseases,the corresponding mathematical model is established to reflect the epidemic law of the disease,so as to understand the overall situation of the epidemic.Considering the influence of stochastic factors on the spread of infectious diseases,this thesis establishes the dynamic equation of stochastic infectious diseases.The main research contents of this thesis are as follows:An SIR model with prevention awareness in a complex network is established,and the vigilance and prevention awareness of infectious diseases are taken into account in the model.Then,by giving a threshold—basic regeneration number R0,the disease-free equilibrium and endemic equilibrium of the system are given.The stability condition of the system at equilibrium point is proved by Lyapunov method.The validity of the theory is verified by simulation.Considering that environmental change will cause the change of infection rate,Markov jump is introduced into the model of chapter 2 to obtain the stochastic SIR model in the network,a threshold similar to the second chapter is given,through which the conditions for the extinction of infectious diseases and the conditions for the persistence of infectious diseases are given.It is proved that the scale of infected patients is normal and ergodic under the condition of the persistence of infectious diseases.The validity of the theory is verified by simulation.A stochastic SEIR model is established under a complex network.Population flow is taken into account in the model and the environment as white noise added to the model.The existence of positive solution of the system is proved stability near the equilibrium point.Then the conditions for the demise of infectious diseases are given.The validity of the theory is verified by simulation.