This paper deals with an epidemiological predator-prey model in which the population of preys is divided into two classes: susceptible and infected prey, and the population of predators is divided into two stage groups: juveniles and adults. The age of maturity introduces a constant delay which leads to a nonlinear system of delayed differential equations.
Sufficient conditions for the asymptotic stability of the five equilibria are established. Considering the delay as a varying parameter, the stability of the positive equilibrium is analyzed. Under some conditions, a Hopf bifurcation occurs when the delay passes through a critical value. Using the normal form and center manifold theory, explicit formulae determining the direction of the bifurcating periodic solutions are provided.
The paper ends with some numerical simulations to illustrate the theoretical results.