Chaos in delay-induced Leslie–Gower prey–predator–parasite model and its control through prey harvesting

Abstract

In this paper we analyze a delay-induced predator–prey–parasite model with prey harvesting, where the predator–prey interaction is represented by Leslie–Gower type model with type II functional response. Infection is assumed to spread horizontally from one infected prey to another susceptible prey following mass action law. Spreading of disease is not instantaneous but mediated by a time lag to take into account the time required for incubation process. Both the susceptible and infected preys are subjected to linear harvesting. The analysis is accomplished in two phases. First we analyze the delay-induced predator–prey–parasite system in absence of harvesting and proved the local & global dynamics of different (six) equilibrium points. It is proved that the delay has no influence on the stability of different equilibrium points except the interior one. Delay may cause instability in an otherwise stable interior equilibrium point of the system and larger delay may even produce chaos if the infection rate is also high. In the second phase, we explored the dynamics of the delay-induced harvested system. It is shown that harvesting of prey population can suppress the abrupt fluctuations in the population densities and can stabilize the system when it exceeds some threshold value.