The dynamics and density function of a stochastic SEIW brucellosis model with Ornstein-Uhlenbeck process

A stochastic SEIW brucellosis model with Ornstein-Uhlenbeck process is investigated. In the model, we consider some of the realities of brucellosis transmission, such as the existence of incubation period and environmental pathogen contamination, and the spread of brucellosis also in incubation period and contaminated environment. The threshold values R0e and R0s for the stochastic extinction of the disease and the existence of a stationary distribution are established. Specifically, if R-0(e) < 1, then brucellosis almost surely exponentially dies out; otherwise, if R-0(s )> 1, then brucellosis is persistent in the mean, and the model also has ergodic property and at least one stationary distribution. Furthermore, when R-0 > 1, where R0 is the basic reproduction number of the corresponding deterministic model, the specific expression of an approximate normal density function around quasi-positive equilibrium is calculated. Finally, numerical examples are presented to illustrate the theoretical results, discuss the change of R0e with the main parameters beta 1, beta 2, alpha and l and examine the relationship between R0 and R0s. The specific expression of the marginal probability density function is obtained through a numerical simulation. The numerical simulation indicates that, in the real world, environmental interference may promote the spread of brucellosis.