Eco‐Epidemiological Mathematical Model Analysis With Time Delays and Hopf Bifurcation

ABSTRACT Ecological and infection predator prey mathematical model is important tool for understanding complex systems and forecasting outcomes biologically. Incorporating saturation mass action incidence rates representing the rate of susceptible prey infection as a function of time along with time delay terms, makes more realistic and reflective of the inherent dynamics in the real‐world systems. This study develops and analyzes delayed ecology model with disease where prey is infected by microparasites, and the predator consume both susceptible and diseased prey. The infection process is assumed to involve a constant time delay, referred to as the infection delay, while the predator reproduction following prey consumption introduces another delay, known as the gestation delay. Qualitative analysis of the model is verified. The consequence of delay terms in the model on the stability of the coexistence fixed point is investigated by treating the delay as a bifurcation parameter. The results indicate the existence of Hopf bifurcation and stability switching as delay cross a certain critical threshold values. Finally, we performed numerical simulations using ODE 45 and DDE 23 codes to support the theoretical and qualitative results in agreement with numerical findings.