Threshold dynamics of a bat-borne rabies model with periodic incubation periods

Bat-borne rabies is a viral infection caused by lyssaviruses. To explore the complex interaction between bats and cattle, we develop a periodic compartment system with seasonality, temperature-dependent incubation period and different control measures. We derive the basic reproduction number R₀ and show it determines the global dynamics. In particular, we prove the non-existence of positive periodic solutions in the critical case where R₀=1. Numerically, we observe that sufficient long time-varying incubation periods could potentially increase the disease outbreak risk.