The Coefficient Of SIR Epidemic Model With Random Disturbances Disease-free Asymptotic Behavior Of Solution

For a long time,various types of infectious diseases bring great disaster,so to understand the spread of infectious disease process and related rules and try to reduce the transmission probability,has a lot of safeguard people’s lives.In this paper,we use SIR model,add random perturbation term and further deduce,to understand the law of the increase or decrease of the number of infected people,to find the effective means to prevent the disease.In the process of constructing the model,the stochastic perturbation term is added,which involves the Lipschitz continuity condition,random process of stopping,Brownian motion,Fatou lemma,and so on.The dynamics model of infectious diseases is one of the research methods,based on the characteristics of population growth,between people,external environment factors,such as the transmission way of the model can reflect the characteristics of infectious diseases.From the perspective of the spread of disease,infectious disease model is to be able to better reflect the advantages of the rule of it,let people aware of infectious diseases in the process of all-round development.Infectious disease model to examine the argument with random disturbance and deduction,the corresponding conclusion,deeper understanding of the disease.A dynamic model of infectious disease is a kind of method research of infectious diseases,through which to understand infectious disease diffusion,analysis of the evolution law of infectious diseases,prevent its spread,provide convenience for the prevention and treatment,is of great practical significance.In this paper,a random perturbation term is added to the model to increase the Brownian motion for the natural mortality,the cure rate of the cured,the cure rate of the disease and the fatality rate of the disease,so that after the disturbance on behalf of the number of new infections,the number of their own death of the number of items remain non-negative.It is deduced that if there is neither exponential increase in population,nor drastic change in the natural mortality rate or rate of reduction,and in particular,no large-scale random population influx,then over time,case fatality rate stable disease tend to disappear.