A periodic two-patch SIS model with time delay and transport-related infection.

In this paper, we propose a periodic SIS epidemic model with time delay and transport-related infection in a patchy environment. The basic reproduction number R0 is derived which determines the global dynamics of the model system: if R0 < 1, the disease-free periodic state is globally attractive while there exists at least one positive periodic state and the disease persists if R0 > 1. Numerical simulations are performed to confirm the analytical results and to explore the dependence of R0 on the transport-related infection parameters and the amplitude of fluctuations.