The global stability of an SIRS model with infection age
Infection age is an important factor affecting the transmission ofinfectious diseases. In this paper, we consider an SIRS modelwith infection age, which is described by a mixed system ofordinary differential equations and partial differentialequations. The expression of the basic reproduction numbe...
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AIMS Press
2013-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.449 |
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| author | Yuming Chen Junyuan Yang Fengqin Zhang |
| author_facet | Yuming Chen Junyuan Yang Fengqin Zhang |
| author_sort | Yuming Chen |
| collection | DOAJ |
| description | Infection age is an important factor affecting the transmission ofinfectious diseases. In this paper, we consider an SIRS modelwith infection age, which is described by a mixed system ofordinary differential equations and partial differentialequations. The expression of the basic reproduction number$\mathscr {R}_0$ is obtained. If $\mathscr{R}_0\le 1$ then themodel only has the disease-free equilibrium, while if$\mathscr{R}_0>1$ then besides the disease-free equilibrium themodel also has an endemic equilibrium. Moreover, if$\mathscr{R}_0<1 then="" the="" disease-free="" equilibrium="" is="" globally="" asymptotically="" stable="" otherwise="" it="" is="" unstable="" if="" mathscr="" r="" _0="">1$ then the endemicequilibrium is globally asymptotically stable under additional conditions. The local stabilityis established through linearization. The global stability of thedisease-free equilibrium is shown by applying the fluctuationlemma and that of the endemic equilibrium is proved by employing Lyapunov functionals. The theoretical results are illustrated with numerical simulations. |
| format | Article |
| id | doaj-art-b4b35ef14ee6477bb5e1e06fff9f6954 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-b4b35ef14ee6477bb5e1e06fff9f69542025-01-24T02:28:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-12-0111344946910.3934/mbe.2014.11.449The global stability of an SIRS model with infection ageYuming Chen0Junyuan Yang1Fengqin Zhang2Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, ShanxiDepartment of Applied Mathematics, Yuncheng University, Yuncheng 044000, ShanxiDepartment of Applied Mathematics, Yuncheng University, Yuncheng 044000, ShanxiInfection age is an important factor affecting the transmission ofinfectious diseases. In this paper, we consider an SIRS modelwith infection age, which is described by a mixed system ofordinary differential equations and partial differentialequations. The expression of the basic reproduction number$\mathscr {R}_0$ is obtained. If $\mathscr{R}_0\le 1$ then themodel only has the disease-free equilibrium, while if$\mathscr{R}_0>1$ then besides the disease-free equilibrium themodel also has an endemic equilibrium. Moreover, if$\mathscr{R}_0<1 then="" the="" disease-free="" equilibrium="" is="" globally="" asymptotically="" stable="" otherwise="" it="" is="" unstable="" if="" mathscr="" r="" _0="">1$ then the endemicequilibrium is globally asymptotically stable under additional conditions. The local stabilityis established through linearization. The global stability of thedisease-free equilibrium is shown by applying the fluctuationlemma and that of the endemic equilibrium is proved by employing Lyapunov functionals. The theoretical results are illustrated with numerical simulations.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.449global stabilitypersistence.sirs modelinfection age |
| spellingShingle | Yuming Chen Junyuan Yang Fengqin Zhang The global stability of an SIRS model with infection age Mathematical Biosciences and Engineering global stability persistence. sirs model infection age |
| title | The global stability of an SIRS model with infection age |
| title_full | The global stability of an SIRS model with infection age |
| title_fullStr | The global stability of an SIRS model with infection age |
| title_full_unstemmed | The global stability of an SIRS model with infection age |
| title_short | The global stability of an SIRS model with infection age |
| title_sort | global stability of an sirs model with infection age |
| topic | global stability persistence. sirs model infection age |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.449 |
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