Dynamics Behavior Of A Stochastic SIR Model With Constant Recruitment

In this paper,we extended some deterministic epidemic model by inducing a whitenoise in the model,and got a stochastic SIR epidemics model, which takes the form ofwhere B(t) is a standard Brownian Motion.First,the uniqueness and existence of the global positive solution of the above modelare proved by Variable transformation and theorem of uniqueness and existence of so-lution of SDE;Second,we discuss the extinction behavior of infectious diseases;Last,weproved the existence of the invariant density of (S(t), I(t)) by using Markov SemigroupTheory and verified that the existence of the invariant density of (S(t), I(t)) by numericalsimulation.