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 [Formula: see text] and [Formula: see text] for the stochastic extinction of the disease and the existence of a stationary distribution are established. Specifically, if [Formula: see text], then brucellosis almost surely exponentially dies out; otherwise, if [Formula: see text], then brucellosis is persistent in the mean, and the model also has ergodic property and at least one stationary distribution. Furthermore, when [Formula: see text], where [Formula: see text] 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 [Formula: see text] with the main parameters [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] and examine the relationship between [Formula: see text] and [Formula: see text]. 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.