Asymptotic Analysis of an Age-Structured Predator–Prey Model with Two Time Delays and Disease in the Prey Species

This paper delves into studying the asymptotic behavior of an age-structured predator–prey model featuring two delays. By incorporating time delays into both the reproductive cycles of predators and the infection dynamics of prey, the model offers a unique perspective to examine ecosystem stability. Initially, the system is formulated as an abstract nondensely defined Cauchy problem, allowing for the derivation of conditions under which equilibria exist. Subsequently, the rigorous establishment of global asymptotic stability for the boundary equilibrium is achieved through a comprehensive analysis of eigenvalue distributions. Additionally, the paper adeptly describes Hopf bifurcation results involving two time delay parameters, utilizing stability switching curves to illuminate the dynamics. To further comprehend these findings, several numerical examples are presented, illustrating the practical implications of the theoretical results.