Controllability of an eco-epidemiological system with disease transmission delay: A theoretical study

This paper deals with the qualitative analysis of a disease transmission delay induced prey predator system in which disease spreads among the predator species only. The growth of the predators' susceptible and infected subpopulations is assumed as modified Leslie-Gower type. Sufficient conditions for the persistence, permanence, existence and stability of equilibrium points are obtained. Global asymptotic stability of the system is investigated around the coexisting equilibrium using a geometric approach. The existence of Hopf bifurcation phenomenon is also examined with respect to some important parameters of the system. The criterion for disease a transmission delay the induced Hopf bifurcation phenomenon is obtained and subsequently, we use a normal form method and the center manifold theorem to examine the nature of the Hopf bifurcation. It is clearly observed that competition among predators can drive the system to a stable from an unstable state. Also the infection and competition among predator population enhance the availability of prey for harvesting when their valuesare high. Finally, some numerical simulations are carried out to illustrate the analytical results.