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Liu Q, Jiang D. Global dynamical behavior of a multigroup SVIR epidemic model with Markovian switching. INT J BIOMATH 2021. [DOI: 10.1142/s1793524521500807] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, we are concerned with the global dynamical behavior of a multigroup SVIR epidemic model, which is formulated as a piecewise-deterministic Markov process. We first obtain sufficient criteria for extinction of the diseases. Then we establish sufficient criteria for persistence in the mean of the diseases. Moreover, in the case of persistence, we find a domain which is positive recurrence for the solution of the stochastic system by constructing an appropriate Lyapunov function with regime switching.
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Affiliation(s)
- Qun Liu
- Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, Jilin Province, P. R. China
| | - Daqing Jiang
- Key Laboratory of Unconventional Oil and Gas Development, China University of Petroleum (East China), Ministry of Education, Qingdao 266580, P. R. China
- College of Science, China University of Petroleum, Qingdao 266580, Shandong Province, P. R. China
- Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, Jeddah, Saudi Arabia
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Feng T, Qiu Z. Global dynamics of deterministic and stochastic epidemic systems with nonmonotone incidence rate. INT J BIOMATH 2019. [DOI: 10.1142/s1793524518501012] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper is devoted to studying the dynamics of a susceptible-infective-latent-infective (SILI) epidemic model that is subject to the combined effects of environmental noise and intervention strategy. We extend the classical SILI epidemic model from a deterministic framework to a stochastic one. For the deterministic case, the global stability analysis of the solution is carried out in terms of the basic reproduction number. For the stochastic case, sufficient conditions for the extinction of diseases are obtained. Then, the existence of stationary distribution and asymptotic behavior of the solution are further studied to illustrate the cycling phenomena of recurrent diseases. Numerical simulations are conducted to verify these analytical results. It is shown that both stochastic noise and intervention strategy contribute to the control of diseases.
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Affiliation(s)
- Tao Feng
- School of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
| | - Zhipeng Qiu
- School of Science, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
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