Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination Disturbance
It is well known that many natural phenomena and human activities do exhibit impulsive effects in the fields of epidemiology. At the same time, compared with a single control strategy, it is obvious that the multiple control strategies are more beneficial to restrain the spread of infectious disease...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/6617911 |
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| _version_ | 1832553049621528576 |
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| author | Yanli Ma Xuewu Zuo |
| author_facet | Yanli Ma Xuewu Zuo |
| author_sort | Yanli Ma |
| collection | DOAJ |
| description | It is well known that many natural phenomena and human activities do exhibit impulsive effects in the fields of epidemiology. At the same time, compared with a single control strategy, it is obvious that the multiple control strategies are more beneficial to restrain the spread of infectious diseases. In this paper, we consider pulse vaccination and pulse elimination strategies at the same time and establish an SIRS epidemic model with standard incidence. Firstly, according to the stroboscopic mapping method of the discrete dynamical system, the disease-free T periodic solution of the model under the condition of pulse vaccination and pulse elimination is obtained. Secondly, the basic reproductive number R0 is defined, and the local asymptotic stability of the disease-free T periodic solution is proved by Floquet theory for R0<1. Finally, based on the impulsive differential inequality theory, the global asymptotic stability of the disease-free T periodic solution is given for R0<1, and the disease dies out eventually. The results show that in order to stop the disease epidemic, it is necessary to choose the appropriate vaccination rate and elimination rate and the appropriate impulsive period. |
| format | Article |
| id | doaj-art-35661ac2bcfb4fbd8a3d569de42f1e3f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-35661ac2bcfb4fbd8a3d569de42f1e3f2025-02-03T05:56:56ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/6617911Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination DisturbanceYanli Ma0Xuewu Zuo1Department of Common CourseDepartment of Common CourseIt is well known that many natural phenomena and human activities do exhibit impulsive effects in the fields of epidemiology. At the same time, compared with a single control strategy, it is obvious that the multiple control strategies are more beneficial to restrain the spread of infectious diseases. In this paper, we consider pulse vaccination and pulse elimination strategies at the same time and establish an SIRS epidemic model with standard incidence. Firstly, according to the stroboscopic mapping method of the discrete dynamical system, the disease-free T periodic solution of the model under the condition of pulse vaccination and pulse elimination is obtained. Secondly, the basic reproductive number R0 is defined, and the local asymptotic stability of the disease-free T periodic solution is proved by Floquet theory for R0<1. Finally, based on the impulsive differential inequality theory, the global asymptotic stability of the disease-free T periodic solution is given for R0<1, and the disease dies out eventually. The results show that in order to stop the disease epidemic, it is necessary to choose the appropriate vaccination rate and elimination rate and the appropriate impulsive period.http://dx.doi.org/10.1155/2024/6617911 |
| spellingShingle | Yanli Ma Xuewu Zuo Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination Disturbance Journal of Mathematics |
| title | Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination Disturbance |
| title_full | Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination Disturbance |
| title_fullStr | Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination Disturbance |
| title_full_unstemmed | Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination Disturbance |
| title_short | Stability Analysis of SIRS Model considering Pulse Vaccination and Elimination Disturbance |
| title_sort | stability analysis of sirs model considering pulse vaccination and elimination disturbance |
| url | http://dx.doi.org/10.1155/2024/6617911 |
| work_keys_str_mv | AT yanlima stabilityanalysisofsirsmodelconsideringpulsevaccinationandeliminationdisturbance AT xuewuzuo stabilityanalysisofsirsmodelconsideringpulsevaccinationandeliminationdisturbance |