Dynamical behavior of stochastic multigroup S-DI-A epidemic models for the transmission of HIV |
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| Authors: | Qun Liu Daqing Jiang Tasawar Hayat Ahmed Alsaedi |
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| Institution: | 1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin 130024, PR 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 537000, PR China;3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;4. College of Science, China University of Petroleum, Qingdao, Shandong 266580, PR China;5. Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000, Pakistan |
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| Abstract: | In this paper, we study two stochastic multigroup S-DI-A epidemic models for the transmission of HIV. For the stochastic S-DI-A epidemic model with periodic coefficients, we first obtain sufficient conditions for persistence in the mean of the disease. Then in the case of persistence, we show that the model admits a positive T-periodic solution by using Khasminskii theory of periodic solution. Moreover, we establish sufficient conditions for exponential extinction of the infectious disease. For the stochastic S-DI-A epidemic model disturbed by both white and telegraph noises, we first establish sufficient conditions for persistence in the mean of the disease. Then in the case of persistence, we obtain sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solutions by constructing a suitable stochastic Lyapunov function with regime switching and we also obtain sufficient conditions for exponential extinction of the system with regime switching. |
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| Keywords: | Corresponding author at: School of Mathematics and Statistics Northeast Normal University Changchun 130024 PR China |
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