Allee effect and delay in a predator-prey mode with prey infected through external source and contact of species

Abstract

We proposed and analyzed a predator-prey model where the prey population was not only infected through contact but also got infection from external sources. In this paper we also considered the allee effect in the susceptible prey population. Time delay effect is an important component in every biological systems and can
not be ignored. The present paper investigate to observe the quantitative and qualitative behavior of the system with gestation delay. It is observed that for a lower infection rate, the system is stable for all delays; but for a higher infection rate, there exists several critical values of delay factor below and above which system is stable and unstable alternatively. It is also observed that delay prevents the extinction of predator population and outbreak of disease. Finally we observe that the instability arising from the gestation delay may be controlled if somehow the growth rate of predator population and external source of infection increase
and predation rate for infected prey decreases. We have also observed that allee will drive all prey species in extinction but delay will save these population from extinction. It is concluded that delay has important role in saving the prey population from extinction.