Alternative prey source coupled with prey recovery enhance stability between migratory prey and their predator in the presence of disease

An eco-epidemiological model is considered where the prey population is migratory in nature. To incorporate the temporal pattern of the avian migration into the model, a time dependent recruitment rate was considered with a general functional response. In the numerical simulation we substitute the general functional response with Holling type-I and Holling type-II functional responses. It was observed that the qualitative behaviour of the system does not depend on the choice of the functional responses. The results showed that the system could be made disease free by either decreasing the contact rate or simultaneously increasing the predation and the recovery rate. Moreover, it was observed that the presence of an alternative food source for the predator population helps in the coexistence of all the species.