Global dynamics of a general class of multi-group epidemic models with latency and relapse
A multi-group model is proposed to describe a general relapse phenomenon of infectious diseasesin heterogeneous populations.In each group, the population is divided intosusceptible, exposed, infectious, and recovered subclasses. A generalnonlinear incidence rate is used in the model. The results sho...
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.99 |
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| author | Xiaomei Feng Zhidong Teng Fengqin Zhang |
| author_facet | Xiaomei Feng Zhidong Teng Fengqin Zhang |
| author_sort | Xiaomei Feng |
| collection | DOAJ |
| description | A multi-group model is proposed to describe a general relapse phenomenon of infectious diseasesin heterogeneous populations.In each group, the population is divided intosusceptible, exposed, infectious, and recovered subclasses. A generalnonlinear incidence rate is used in the model. The results show that the global dynamics are completelydetermined by the basic reproduction number $R_0.$ In particular, a matrix-theoretic method is used to provethe global stability of the disease-free equilibrium when $R_0\leq1,$while a new combinatorial identity (Theorem 3.3 in Shuai and vanden Driessche [29]) in graph theory is applied to provethe global stability of the endemic equilibrium when $R_0>1.$We would like to mention that by applying the new combinatorial identity, a graph of 3n (or 2n+m) vertices can be converted intoa graph of n vertices in order to deal with the global stability of the endemic equilibrium in this paper. |
| format | Article |
| id | doaj-art-ec5b463921f9469988c9cf6f0d6a9031 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-ec5b463921f9469988c9cf6f0d6a90312025-01-24T02:31:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-011219911510.3934/mbe.2015.12.99Global dynamics of a general class of multi-group epidemic models with latency and relapseXiaomei Feng0Zhidong Teng1Fengqin Zhang2College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, ShanxiA multi-group model is proposed to describe a general relapse phenomenon of infectious diseasesin heterogeneous populations.In each group, the population is divided intosusceptible, exposed, infectious, and recovered subclasses. A generalnonlinear incidence rate is used in the model. The results show that the global dynamics are completelydetermined by the basic reproduction number $R_0.$ In particular, a matrix-theoretic method is used to provethe global stability of the disease-free equilibrium when $R_0\leq1,$while a new combinatorial identity (Theorem 3.3 in Shuai and vanden Driessche [29]) in graph theory is applied to provethe global stability of the endemic equilibrium when $R_0>1.$We would like to mention that by applying the new combinatorial identity, a graph of 3n (or 2n+m) vertices can be converted intoa graph of n vertices in order to deal with the global stability of the endemic equilibrium in this paper.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.99global stabilitymultigroup epidemic modelnonlinear incidencelyapunov function. |
| spellingShingle | Xiaomei Feng Zhidong Teng Fengqin Zhang Global dynamics of a general class of multi-group epidemic models with latency and relapse Mathematical Biosciences and Engineering global stability multigroup epidemic model nonlinear incidence lyapunov function. |
| title | Global dynamics of a general class of multi-group epidemic models with latency and relapse |
| title_full | Global dynamics of a general class of multi-group epidemic models with latency and relapse |
| title_fullStr | Global dynamics of a general class of multi-group epidemic models with latency and relapse |
| title_full_unstemmed | Global dynamics of a general class of multi-group epidemic models with latency and relapse |
| title_short | Global dynamics of a general class of multi-group epidemic models with latency and relapse |
| title_sort | global dynamics of a general class of multi group epidemic models with latency and relapse |
| topic | global stability multigroup epidemic model nonlinear incidence lyapunov function. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.99 |
| work_keys_str_mv | AT xiaomeifeng globaldynamicsofageneralclassofmultigroupepidemicmodelswithlatencyandrelapse AT zhidongteng globaldynamicsofageneralclassofmultigroupepidemicmodelswithlatencyandrelapse AT fengqinzhang globaldynamicsofageneralclassofmultigroupepidemicmodelswithlatencyandrelapse |