Model formulation and oscillatory patterns in immune-pathogen dynamics during Brucellosis infection

Brucellosis, a global zoonosis imposing major health and economic burdens, is clinically marked by recurrent undulant fever linked to Brucella’s persistence within macrophages. To decipher the immune-pathogen dynamics underlying this fever periodicity, this study develops a novel mathematical model that integrates macrophage self-renewal, logistic growth constrained by cellular carrying capacity, and intracellular Brucella replication. Stability and bifurcation analyses reveal two crucial thresholds: one for infection persistence, requiring $R_0>1$, and another for the emergence of undulant fever, triggered by a supercritical Hopf bifurcation. This bifurcation occurs when the macrophage self-renewal rate ($r$) surpasses its mortality rate ($d$) and the infection rate ($\theta$) lies in a critical range, marking a transition from stable equilibrium to stable limit cycles. These periodic oscillations, stemming from a dynamic imbalance between immune regeneration and bacterial proliferation, provide a direct mechanistic explanation for recurrent febrile episodes. Counterintuitively, excessive macrophage renewal or carrying capacity can destabilize the system, exacerbating febrile cycles. Our findings posit that interventions simultaneously preventing immune resource exhaustion and curbing intracellular bacterial survival could suppress these pathological oscillations, thereby proposing novel perspectives for managing chronic brucellosis.