Modeling and dynamics of Brucella infection-induced macrophage apoptosis inhibition

Brucella is an intracellular bacterium that causes the widespread zoonotic disease brucellosis. Within their hosts, Brucella has evolved various immune evasion strategies, including the ability to survive and replicate within host cells, especially within macrophages. This leads brucellosis from an acute phase to a chronic phase that is difficult to cure. In order to explore the key factors for the survival of Brucella and the mechanisms of persistent chronic infection, a mathematical model is developed to characterize the interactions between Brucella and macrophages, which incorporates a saturable apoptosis-inhibiting function within an infected host. The dynamics are well investigated in mathematics such as the invariance and boundedness, the existence and stability of equilibria, the bifurcation dynamics, and the threshold criteria for the clearance of Brucella infection. In particular, it is elaborated that the model can undergo forward and backward bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation of codimension 2 by applying the central manifold theorem and normal form theory. Numerical analyses indicate that the presence of bistability complicates the clearance processes of Brucella. In addition, the infection rate of Brucella and the baseline apoptosis rate of infected macrophages are identified as key factors in determining Brucella clearance, the persistence of chronic infection, and the occurrence of undulating fever. The main findings highlight that increasing immune clearance capacity and reducing the virulence of Brucella are critical for controlling Brucella infections.