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

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