Dynamics of a stochastic SIR epidemic model with distributed delay and degenerate diffusion |
| |
| Institution: | 1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, Jilin Province, PR China;2. Key Laboratory of Unconventional Oil and Gas Development, China University of Petroleum (East China), Ministry of Education, Qingdao 266580, PR China;3. College of Science, China University of Petroleum, Qingdao 266580, Shandong Province, PR China;4. Nonlinear Analysis and Applied Mathematics (NAAM)Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;5. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan;1. Department of Mathematics and Statistics, College of Science, King Faisal University, P.O Box 400, Al-Hasa 31982, Saudi Arabia;2. Department of Mathematics, COMSATS University Park Road Chak Shahzad, Islamabad, 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. College of Arts and Sciences, Shanghai Polytechnic University, Shanghai 201209, China;2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin 130024, PR China;2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;3. College of Science, China University of Petroleum, Qingdao, Shandong 266580, PR China;4. Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000, Pakistan |
| |
| Abstract: | In this paper, we study a stochastic SIR epidemic model with distributed delay and degenerate diffusion. Firstly, we transform the stochastic model into an equivalent system which contains three equations. Since the diffusion matrix is degenerate, the uniform ellipticity condition is not satisfied. The Markov semigroup theory is used to obtain the existence and uniqueness of a stable stationary distribution. We verify the densities of the distributions of the solutions can converge in L1 to an invariant density. Then we establish sufficient conditions for extinction of the disease. Some examples and numerical simulations are introduced to illustrate our analytical results. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
