An eco-epidemic model with seasonal variability: a non-autonomous model

Seasonal variability strongly affects the animal population in wildlife. It becomes essential to model seasonality in eco-epidemic dynamics to know the effect of system parameters in a periodic environment. This article presents a set of non-autonomous differential equations with time-varying disease transmission rates among prey and predators, the mortality rate of a diseased predator, the predation rate of healthy prey, and an additional food supply. The positiveness, boundedness, and presence of solution are derived. We have proved that the infection-free state is stable if periodic basic reproduction number R-C (t) < 1. The stability of the coexistence state is shown at R-C (t) > 1 using the Poincare map and comparison theory. The significance of the parameters related to disease transmission and prevalence is described using sensitivity analysis. Numerical simulation verified our analytical findings and proved that the predator control strategies in the periodic environment via controlling predation rate, disease transmission rate among predators, and death rate of diseased prey lead the system towards an infection-free environment.