Study On The Stochastic Brucellosis Models Driven By White Noise And L(?)vy Noise

Brucellosis is a natural zoonotic infectious disease caused by brucella,it has occurred between humans and animals in most provinces(autonomous regions and municipalities directly under the central government)in China,among which sheep,cattle and pigs are the main sources of infection for humans and animals.In recent years,brucellosis epidemic situation showed a trend of rapid recovery and expansion in China,due to the influence of social factors such as the increase of livestock trade and the frequent movement of livestock.So,it is well known that brucellosis not only brings great economic losses to the livestock industry,but it also poses a major threat to the public health.The theoretical research on the mathematical model of infectious diseases is an important method for the theoretical quantitative research of infectious disease,it can help people to understand some global states in the process of transmission,which has certain theoretical and practical significance for the prediction and prevention of diseases.As we all know,in our real life,brucellosis is inevitably affected by random disturbances during its transmission.Therefore,based on the deterministic model of brucellosis proposed by some researchers,three stochastic models of brucellosis were established in this paper by considering the environment white noise and L(?)vy noise in the transmission process of brucellosis,the main research content of this paper includes the following three aspects:In the first part(corresponding to Chapter 3),we study a stochastic sheep brucellosis model with immigration.We use It(?)'s formula,the large number the-orem for martingales,Gronwall's inequality,the comparison theorem of stochastic differential equation,etc.to study the existence of global positive solution,and the sufficient conditions for the brucellosis extinction and persistence in the mean.In addition,we numerically simulate the solution pathes for stochastic model and find that stochastic perturbation is contribute to extinction of brucellosis.In the second part(corresponding to Chapter 4),the L(?)vy noise is added on the model driven by environment white noise in the third part.By using Poisson-It^o's formula and constructing appropriate Lyapunov functions,we analyse the asymp-totic behavior of the solutions for the stochastic model around P~0and P~*,where P~0 and P~*are the disease-free equilibrium and the endemic equilibrium of the de-terministic model which corresponded by stochastic model,respectively.In the third part(corresponding to Chapter 5),we consider a stochastic two-patch brucellosis model.We obtain a series of stochastic threshold dynamics results,incorporating extinction of the disease,existence of a unique ergodic stationary distribution of the positive solution to systems in both path 1 and 2.Finally,we build numerical simulations to support the theoretical results.