A Delay Differential Equation Model of A Predator Prey System with a Transmissible Disease in the Prey Population

Abstract

The present paper deals with the problem of a predator-prey system with a disease in the prey population (interpreted to be phytoplankton cells) out of which the infected cells neither reproduce nor recover. We use Liapunov functional approach to establish persistence criterion for the three populations, namely, sound and infected prey, and predator. In the three-dimensional system of integrodifferential equations model, integral terms represent that the process of infection is not instantaneous but takes some time to form a new group of infected phytoplankton cells from susceptible phytoplankton cells.