Dynamics of epidemic models with asymptomatic infection and seasonal succession
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and evaluated directly for this model, and uniform persistence of the di...
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017073 |
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| author | Yilei Tang Dongmei Xiao Weinian Zhang Di Zhu |
| author_facet | Yilei Tang Dongmei Xiao Weinian Zhang Di Zhu |
| author_sort | Yilei Tang |
| collection | DOAJ |
| description | In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and evaluated directly for this model, and uniform persistence of the disease and threshold dynamics are obtained. Specially, global dynamics of the model without seasonal force are studied. It is shown that the model has only a disease-free equilibrium which is globally stable if $\mathcal{R}_0≤ 1$, and as $\mathcal{R}_0 \gt 1$ the disease-free equilibrium is unstable and there is an endemic equilibrium, which is globally stable if the recovering rates of asymptomatic infectives and symptomatic infectives are close. These theoretical results provide an intuitive basis for understanding that the asymptomatically infective individuals and the seasonal disease transmission promote the evolution of the epidemic, which allow us to predict the outcomes of control strategies during the course of the epidemic. |
| format | Article |
| id | doaj-art-f0b09400a5a3424fb96f876ad296ad64 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f0b09400a5a3424fb96f876ad296ad642025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61407142410.3934/mbe.2017073Dynamics of epidemic models with asymptomatic infection and seasonal successionYilei Tang0Dongmei Xiao1Weinian Zhang2Di Zhu3School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, ChinaSchool of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, ChinaYangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaSchool of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, ChinaIn this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and evaluated directly for this model, and uniform persistence of the disease and threshold dynamics are obtained. Specially, global dynamics of the model without seasonal force are studied. It is shown that the model has only a disease-free equilibrium which is globally stable if $\mathcal{R}_0≤ 1$, and as $\mathcal{R}_0 \gt 1$ the disease-free equilibrium is unstable and there is an endemic equilibrium, which is globally stable if the recovering rates of asymptomatic infectives and symptomatic infectives are close. These theoretical results provide an intuitive basis for understanding that the asymptomatically infective individuals and the seasonal disease transmission promote the evolution of the epidemic, which allow us to predict the outcomes of control strategies during the course of the epidemic.https://www.aimspress.com/article/doi/10.3934/mbe.2017073epidemic modelasymptomatic infectionseasonal successionbasic reproduction numberthreshold dynamics |
| spellingShingle | Yilei Tang Dongmei Xiao Weinian Zhang Di Zhu Dynamics of epidemic models with asymptomatic infection and seasonal succession Mathematical Biosciences and Engineering epidemic model asymptomatic infection seasonal succession basic reproduction number threshold dynamics |
| title | Dynamics of epidemic models with asymptomatic infection and seasonal succession |
| title_full | Dynamics of epidemic models with asymptomatic infection and seasonal succession |
| title_fullStr | Dynamics of epidemic models with asymptomatic infection and seasonal succession |
| title_full_unstemmed | Dynamics of epidemic models with asymptomatic infection and seasonal succession |
| title_short | Dynamics of epidemic models with asymptomatic infection and seasonal succession |
| title_sort | dynamics of epidemic models with asymptomatic infection and seasonal succession |
| topic | epidemic model asymptomatic infection seasonal succession basic reproduction number threshold dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017073 |
| work_keys_str_mv | AT yileitang dynamicsofepidemicmodelswithasymptomaticinfectionandseasonalsuccession AT dongmeixiao dynamicsofepidemicmodelswithasymptomaticinfectionandseasonalsuccession AT weinianzhang dynamicsofepidemicmodelswithasymptomaticinfectionandseasonalsuccession AT dizhu dynamicsofepidemicmodelswithasymptomaticinfectionandseasonalsuccession |