An SIS epidemic model in a patchy environment with pulse vaccination and quarantine

An SIS epidemic model in an m-patch environment with pulse vaccination and quarantine at two different fixed moments is formulated by impulsive differential equations in this paper. The sufficient conditions for the extinction and persistence of the disease are derived and the threshold value R0 is obtained by using the persistence theory of impulsive systems, the impulsive-type Floquet theory and the perturbation techniques. That is, the infection-free periodic solution is globally asymptotically stable if R0<1, and the impulsive system becomes uniformly persistent if R0>1. When m=2, two special cases are considered to illustrate joint impact of the pulse vaccination and quarantine and population mobility on the disease dynamics. Numerical simulations are given to show the effectiveness of the theoretical results.