Analysis of a nonautonomous model for migratory birds with saturation incidence rate

In this paper, an eco-epidemiological model is newly proposed to consider the role of migratory birds by incorporating the temporal pattern of the avian migration into the model. In the new model, population of birds varies because they are migratory in nature. Under quite weak assumptions, sufficient conditions for the permanence and extinction of the disease is obtained. Moreover, by constructing a Liapunov function, the global attractivity of the model is discussed.

► We model a nonautonomous eco-epidemiological system with saturation contact rate.
► The sufficient conditions for permanence, extinction and global attractivity of the model are obtained.
► A globally attractive periodic solution exists for the periodic system by numerical simulation.
► Increasing the amplitude of periodic recovery rate reduces the risk of epidemic prevalence.