Abstract

The study presents a mathematical model of the dynamics of host–pathogen interaction that incorporates immune response feedback mechanisms. To gain insights into the evolution and persistence of pathogens within host systems and the innate and adaptive immune responses that regulate them. It uses the model to include non-linear differential equations that describe the time evolution of susceptible host cells, infected cells, pathogen load and immune effector cells. This study differs from classical models, that assume static immune effects and focuses on feedback-driven immune activation and suppression, reflecting more realistic biological behaviour. The model for biological processes such as infection rate, pathogen replication, immune cell recruitment, and pathogen clearance. pathogen concentration is modelled dynamically, and, as such, a feedback loop is included: the body's immune system can be activated at a certain threshold and can become exhausted when pathogen concentration is high. Stability analysis is used to determine the equilibrium points for the disease-free and endemic states. Local stability can be determined by eigenvalue analysis of the Jacobian matrix, which indicates parameter ranges in which infection persists or is cleared. The system behaviour is explored through numerical simulations with varying levels of virulence and immune response strengths. The results show that the system is stable and infection is eradicated when the immune feedback is strong. Still, oscillating solutions or an infection steady state can occur with weaker or lagged immune feedback. Sensitivity analysis also reveals that infection rate and immune activation threshold are key parameters that affect disease outcome. The study offers theoretical background for understanding the complex interaction among host, pathogen, and immune system, and provides insights into the mechanisms of disease progression. It also points out the role of immune feedback regulation in the control of infections and the prevention of chronic disease conditions. The results can apply to infectious disease modelling, optimization of vaccine strategy, and design of immunotherapy, where controlling immune response dynamics is key to a successful therapeutic outcome.