A study of harvesting in a predator–prey model with disease in both populations

Disease control by managers is a crucial response to emerging epidemics, and in the context of global change, emerging risks associated with parasites, invasive species, and infectious diseases are an important issue especially for developing countries. Our objective is to provide a mathematical framework to study the response of a predator–prey model to a disease in both populations and harvesting of prey species. We have worked out the conditions for local stability of the equilibrium points as well as persistence of the system. We have derived the ecological and disease basic reproduction numbers. These enable us to determine the community structure of the system. Harvesting may play a crucial role in a host–parasite system, and reasonable harvesting can remove parasite burden from the host. Our numerical results reveal that the reasonable harvesting prevents the oscillations of the species. We conclude that harvesting can be an effective strategy for controlling the spread of disease.