Dynamics of hybrid switching DS-I-A epidemic model

Songnan Liu; Daqing Jiang; Xiaojie Xu; Tasawar Hayat; Bashir Ahmad

doi:10.1038/s41598-017-11901-x

Dynamics of hybrid switching DS-I-A epidemic model

Sci Rep. 2017 Sep 26;7(1):12332. doi: 10.1038/s41598-017-11901-x.

Authors

Songnan Liu¹, Daqing Jiang^{2

3}, Xiaojie Xu⁴, Tasawar Hayat^{5

6}, Bashir Ahmad⁵

Affiliations

¹ College of Science, China University of Petroleum (East China), Qingdao, 266580, China.
² College of Science, China University of Petroleum (East China), Qingdao, 266580, China. daqingjiang2010@hotmail.com.
³ Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia. daqingjiang2010@hotmail.com.
⁴ College of Science, China University of Petroleum (East China), Qingdao, 266580, China. xuxiaojie77@sohu.com.
⁵ Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia.
⁶ Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan.

Abstract

In this paper, we investigate a stochastic hybrid switching DS-I-A epidemic model. The extinction and the prevalence of the disease are discussed, and so, the threshold is given. Furthermore, the sufficient conditions for the existence of positive recurrence of the solutions are established by stochastic Lyapunov functions. At last, some examples and simulations are provided to illustrate our results.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Acquired Immunodeficiency Syndrome / epidemiology*
Computer Simulation
Epidemics*
Humans
Markov Chains
Models, Biological*
Nonlinear Dynamics
Prevalence