Epidemic models for complex networks with demographics
In this paper, we propose and study network epidemic models withdemographics for disease transmission. We obtain the formula of thebasic reproduction number $R_{0}$ of infection for an SIS model withbirths or recruitment and death rate. We prove that if $R_{0}\leq1$,infection-free equilibrium of SIS...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1295 |
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| author | Zhen Jin Guiquan Sun Huaiping Zhu |
| author_facet | Zhen Jin Guiquan Sun Huaiping Zhu |
| author_sort | Zhen Jin |
| collection | DOAJ |
| description | In this paper, we propose and study network epidemic models withdemographics for disease transmission. We obtain the formula of thebasic reproduction number $R_{0}$ of infection for an SIS model withbirths or recruitment and death rate. We prove that if $R_{0}\leq1$,infection-free equilibrium of SIS model is globally asymptoticallystable; if $R_{0}>1$, there exists a unique endemic equilibrium whichis globally asymptotically stable. It is also found thatdemographics has great effect on basic reproduction number $R_{0}$.Furthermore, the degree distribution of population varies with timebefore it reaches the stationary state. |
| format | Article |
| id | doaj-art-8c631878dc7a4b4aab204ad1021f3be0 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8c631878dc7a4b4aab204ad1021f3be02025-01-24T02:29:00ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-08-011161295131710.3934/mbe.2014.11.1295Epidemic models for complex networks with demographicsZhen Jin0Guiquan Sun1Huaiping Zhu2Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030051Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030051LAMPS and CDM, Department of Mathematics and Statistics, York University, Toronto, ON, M3J1P3In this paper, we propose and study network epidemic models withdemographics for disease transmission. We obtain the formula of thebasic reproduction number $R_{0}$ of infection for an SIS model withbirths or recruitment and death rate. We prove that if $R_{0}\leq1$,infection-free equilibrium of SIS model is globally asymptoticallystable; if $R_{0}>1$, there exists a unique endemic equilibrium whichis globally asymptotically stable. It is also found thatdemographics has great effect on basic reproduction number $R_{0}$.Furthermore, the degree distribution of population varies with timebefore it reaches the stationary state.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1295complex networksdemographicsepidemic modelsbasic reproduction numberglobal stability. |
| spellingShingle | Zhen Jin Guiquan Sun Huaiping Zhu Epidemic models for complex networks with demographics Mathematical Biosciences and Engineering complex networks demographics epidemic models basic reproduction number global stability. |
| title | Epidemic models for complex networks with demographics |
| title_full | Epidemic models for complex networks with demographics |
| title_fullStr | Epidemic models for complex networks with demographics |
| title_full_unstemmed | Epidemic models for complex networks with demographics |
| title_short | Epidemic models for complex networks with demographics |
| title_sort | epidemic models for complex networks with demographics |
| topic | complex networks demographics epidemic models basic reproduction number global stability. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.1295 |
| work_keys_str_mv | AT zhenjin epidemicmodelsforcomplexnetworkswithdemographics AT guiquansun epidemicmodelsforcomplexnetworkswithdemographics AT huaipingzhu epidemicmodelsforcomplexnetworkswithdemographics |