Modeling and dynamics of <i>Brucella</i> infection with macrophage apoptosis inhibition and immune recovery

Brucella is a facultative intracellular bacterium being responsible for brucellosis, a zoonotic disease characterized by chronicity and frequent relapse. To identify the key factors governing the clearance or persistence of Brucella infection within the host, a mathematical model is developed that incorporates bacterial virulence, macrophage apoptosis, necrosis and immune recovery mechanisms. A deterministic system and its stochastic counterpart are derived to capture the infection dynamics under both deterministic and fluctuating immune responses. The deterministic system admits very rich dynamics and undergoes forward, backward, pitchfork, Hopf and codimension-2 Bogdanov–Takens bifurcations, which reflect the intricate transitions between infection clearance and persistence. The stochastic model has a unique global positive solution, exhibits persistence and possesses a unique ergodic stationary distribution, emphasizing the critical role of intrinsic immune noise. Numerical results indicate that the infection and apoptosis rates determine clearance thresholds, while immune recovery and necrosis regulate the severity and stability of infection. Furthermore, immune recovery of infected macrophages may amplify oscillatory dynamics, while stochastic perturbations can sustain persistent infection even when the basic reproduction number falls below unity. The key findings underscore the interplay between immune regulation and intracellular persistence, and offer insight into the mechanisms driving chronic Brucella infection.