Stochasticity may shape chronic infection outcomes of brucellosis: A macrophage–brucella model with Ornstein–Uhlenbeck process

Brucella is a facultative intracellular pathogen, and its interactions with macrophages play a critical role in chronic infection. We propose a deterministic dynamical model describing brucella infection of macrophages, derive the infection threshold R 0 , and prove the global asymptotic stability of the infection-free equilibrium E 0 and the chronic infection equilibrium E ∗ . Then, the logarithmic Ornstein–Uhlenbeck process is utilized to describe stochastic fluctuations in the infection rate. We establish the existence and uniqueness of the global solution, derive sufficient conditions for stochastic extinction, and prove the existence of at least one stationary distribution. Furthermore, we derive a local Gaussian approximation near the quasi-equilibrium and characterize its covariance matrix. Numerical simulations support the theoretical results and show that stochasticity influences both extinction probability and long-term bacterial burden. In particular, different stochastic realizations under similar parameter settings may lead to pathogen clearance or chronic infection, providing a possible explanation for differentiated outcomes following similar exposure. Notably, the effect of noise intensity on infection outcome is non-monotonic. These findings provide a quantitative framework for understanding differentiated outcomes in chronic brucellosis.