A mathematical study of eco-epidemiological model with effect of harvesting and allee

Abstract

In the present study we have considered a predator-prey model with disease in both population. We have also considered the harvesting in all species and allee in the susceptible prey species. We have worked out the conditions for which the equilibrium points exists and local stability of equilibrium points. We have derived the conditions for persistence of all species. Our numerical simulation results reveals the global behaviors of our system. Disease in prey species accelerates the system to produce limit cycle oscillations and disease in predator species stabilizes the oscillatory system. harvesting in the species also stabilized the oscillatory system. Harvesting in the both species can remove the disease from both population. If we increase the values of allee parameter we have observed the exchange of stability of some important equilibrium points.