Time delay factor can be used as a key factor for preventing the outbreak of a disease—Results drawn from a mathematical study of a one season eco-epidemiological model

Chatterjee and Chattopadhyay [Role of migratory bird population in an simple eco-epidemiological model, Math. Comp. Model. Dyn. Syst., in press] proposed and analyzed a one season eco-epidemiological model of susceptible and infective prey together with their predators. In such systems, time lags due to the gestation of the infective prey are of importance. In this paper we modify and analyze their model by taking this factor into consideration. Our analysis shows that the outbreak of the disease can be controlled by a careful and suitable increment of the time lag factor. Moreover, to preserve the stability of the coexisting equilibrium, the time lag factor plays an important role. To substantiate our analytical results, extensive numerical simulations are performed for a hypothetical set of parameter values.