Affiliations: College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, China
Correspondence:
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Corresponding author. Zhiming Li, College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, China. E-mail: [email protected].
Abstract: Li et al. [1] applied uncertain differential equation (UDE) to study a class of susceptible-infectious-susceptible (SIS) epidemic model with the bilinear incidence rate and constant population size. In this paper, we study an uncertain SIS epidemic model with standard incidence and demography. By scale transformation, the deterministic and uncertain proportion epidemic models are introduced. Solutions of these models and α-paths of uncertain model are given. Further, under threshold conditions, we discuss extinction and permanence of the disease and reveal relationship of the deterministic and uncertain models. Some examples are provided to illustrate these results.
Keywords: Standard incidence, SIS epidemic model, uncertain differential equation, Liu process, α-path
