Abstract
In this paper, we establish a new fractional order SIS (frSIS) model by way of continuous time random walk. The value of this study lies in two aspects. Mathematically, we provide a framework for the global stability of the frSIS model, and prove that the basic reproduction number R0 can be used to govern the dynamics of the frSIS model. If R0<1, the disease-free equilibrium of the model is globally asymptotically stable; if R0>1, the endemic equilibrium of the model is globally asymptotically stable. And epidemiologically, we find that, in order to control the spread of the disease, we must decrease the death rate and the average infectious period to make the disease go to extinction, which can provide us with some useful control strategies to regulate disease dynamics.
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