Study On The Dynamic Properties Of Stochastic Brucellosis Model

Brucellosis,also known as Mediterranean relaxation fever,Maltese fever,wave fever or wavy fever,is a zoonotic chronic infectious disease caused by brucellosis in sheep,cattle,pigs,dogs and humans.It is an important cause of livestock production and reproductive loss,which not only causes serious economic losses,but also can infect human beings.Dynamic model is an important tool in epidemiological research of infectious diseases.The deterministic model of brucellosis has been studied with good results.However,in real life,the spread of disease is inevitably affected by environmental random factors.This paper considers three kinds of stochastic models of brucellosis under the influence of environmental white noise and Markov switching.The main contents are as follows:1.In the first part,we discussed the stochastic brucellosis model,use It(?)’s formula,the large number theorem,we get the existence and uniqueness of positive solution of the model,by using Lyapunov function,established sufficient condition of disease extinction and stationary distribution,and made a numerical simulation to verify the conclusion.2.In the second part,a model of stochastic brucellosis model with imperfect vaccination is discussed.we get the existence and uniqueness of positive solution of the model,by using Lyapunov function,established sufficient condition of disease extinction and stationary distribution.Finally,the numerical model is used to verify the above results.3.In the third part,we introduce environmental white noise and Markov chain into the deterministic brucellosis model,get existence and uniqueness of positive solution,by using Lyapunov function established sufficient condition of stationary distribution.