In this paper, we study an SIS epidemic patch model with media delay. We define the basic reproduction number $\mathcal{R}_0$ and show that the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0<1$ and the disease is uniformly persistent if $\mathcal{R}_0>1$. When the dispersal rates of susceptible and infected populations are identical and less than a critical value, we prove that the limiting model has a unique positive equilibrium, and analyze the stability of the positive equilibrium and the local and global existence of Hopf bifurcations. Finally, some numerical simulations are performed.
MSC 2010: 92D25, 92D50, 34K13, 34K18