Comparison of three SIS epidemic models: deterministic, stochastic and uncertain

Article type: Research Article

Authors: Li, Zhiming | Teng, Zhidong^{; *} | Hong, Dujun | Shi, Xiaoping

Affiliations: College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, China

Correspondence: [*] Corresponding author. Zhidong Teng, College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China. E-mail: zhidong@xju.edu.cn.

Abstract: This paper applies uncertain theory to establish an uncertain differential equation (UDS) SIS epidemic model, comparing with deterministic and stochastic SIS models. Solution of the UDE model is obtained. Threshold conditions are derived for permanence and extinction of disease by the corresponding α-paths, which reveal relationships of three models. Numerical simulations are given to illustrate these results.

Keywords: Deterministic model, stochastic model, uncertain model, Liu process, α-path

DOI: 10.3233/JIFS-18007

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 5, pp. 5785-5796, 2018