Stationary distribution and extinction of a stochastic SIRI epidemic model with relapse |
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| Authors: | Qun Liu Tasawar Hayat Bashir Ahmad |
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| Institution: | 1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin, P.R. China;2. School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, Guangxi, P.R. China;3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;4. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan |
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| Abstract: | In this paper, we study the dynamics of a stochastic Susceptible-Infective-Removed-Infective (SIRI) epidemic model with relapse. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Moreover, sufficient conditions for extinction of the disease are also obtained. |
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| Keywords: | Stochastic SIRI epidemic model stationary distribution and ergodicity extinction Lyapunov function |
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