Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations
In this paper, the asymptotic behavior of a multigroup SEIR model with stochastic perturbations and nonlinear incidence rate functions is studied. First, the existence and uniqueness of the solution to the model we discuss are given. Then, the global asymptotical stability in probability of the mode...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/9367879 |
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| _version_ | 1850172568997199872 |
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| author | Feng Wang Shan Wang Youhua Peng |
| author_facet | Feng Wang Shan Wang Youhua Peng |
| author_sort | Feng Wang |
| collection | DOAJ |
| description | In this paper, the asymptotic behavior of a multigroup SEIR model with stochastic perturbations and nonlinear incidence rate functions is studied. First, the existence and uniqueness of the solution to the model we discuss are given. Then, the global asymptotical stability in probability of the model with R0<1 is established by constructing Lyapunov functions. Next, we prove that the disease can die out exponentially under certain stochastic perturbation while it is persistent in the deterministic case when R0>1. Finally, several examples and numerical simulations are provided to illustrate the dynamic behavior of the model and verify our analytical results. |
| format | Article |
| id | doaj-art-d0029eadb07342209fdd08a4904885a2 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d0029eadb07342209fdd08a4904885a22025-08-20T02:20:03ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/93678799367879Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic PerturbationsFeng Wang0Shan Wang1Youhua Peng2School of Mathematics and Statistics, Central South University, 410083 Changsha, ChinaDepartment of Mathematics, Pingxiang University, 337000 Pingxiang, ChinaDepartment of Mathematics, Pingxiang University, 337000 Pingxiang, ChinaIn this paper, the asymptotic behavior of a multigroup SEIR model with stochastic perturbations and nonlinear incidence rate functions is studied. First, the existence and uniqueness of the solution to the model we discuss are given. Then, the global asymptotical stability in probability of the model with R0<1 is established by constructing Lyapunov functions. Next, we prove that the disease can die out exponentially under certain stochastic perturbation while it is persistent in the deterministic case when R0>1. Finally, several examples and numerical simulations are provided to illustrate the dynamic behavior of the model and verify our analytical results.http://dx.doi.org/10.1155/2020/9367879 |
| spellingShingle | Feng Wang Shan Wang Youhua Peng Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations Discrete Dynamics in Nature and Society |
| title | Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations |
| title_full | Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations |
| title_fullStr | Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations |
| title_full_unstemmed | Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations |
| title_short | Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations |
| title_sort | asymptotic behavior of multigroup seir model with nonlinear incidence rates under stochastic perturbations |
| url | http://dx.doi.org/10.1155/2020/9367879 |
| work_keys_str_mv | AT fengwang asymptoticbehaviorofmultigroupseirmodelwithnonlinearincidenceratesunderstochasticperturbations AT shanwang asymptoticbehaviorofmultigroupseirmodelwithnonlinearincidenceratesunderstochasticperturbations AT youhuapeng asymptoticbehaviorofmultigroupseirmodelwithnonlinearincidenceratesunderstochasticperturbations |