Asymptotic behaviors of stochastic epidemic models with jump-diffusion |
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| Institution: | 1. Department of Mathematics, Vinh University, 182 Le Duan, Vinh, Nghe An, Vietnam;2. Department Environmental Science, Nara Women’s University, Kita-Uoya Nishimachi, Nara 630-8506, Japan;3. Department of Mathematics, Mechanics and Informatics, Hanoi National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam;1. School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, P.R. China;2. School of Mathematics and Information Science, Guangxi Universities Key Lab of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, Guangxi 537000, P.R. China;3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 121589, Saudi Arabia;4. College of Science, China University of Petroleum (East China), Qingdao 266580, P.R. China;5. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan;1. School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024, PR China;2. School of Mathematics and Information Science, Guangxi Universities Key Lab 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, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 121589, Saudi Arabia;4. College of Science, China University of Petroleum (East China), Qingdao 266580, PR China;5. Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad 44000, Pakistan;1. School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;1. College of Science, China University of Petroleum (East China), Qingdao 266580, P.R. China;2. Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;3. Department of Mathematics, Quaid-i-Azam University 45320, Isamabad 44000, Pakistan |
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| Abstract: | In this paper, we classify the asymptotic behavior for a class of stochastic SIR epidemic models represented by stochastic differential systems where the Brownian motions and Lévy jumps perturb to the linear terms of each equation. We construct a threshold value between permanence and extinction and develop the ergodicity of the underlying system. It is shown that the transition probabilities converge in total variation norm to the invariant measure. Our results can be considered as a significant contribution in studying the long term behavior of stochastic differential models because there are no restrictions imposed to the parameters of models. Techniques used in proving results of this paper are new and suitable to deal with other stochastic models in biology where the noises may perturb to nonlinear terms of equations or with delay equations. |
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