Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment
An epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/647853 |
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| _version_ | 1850226767053193216 |
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| author | Yakui Xue Junfeng Wang |
| author_facet | Yakui Xue Junfeng Wang |
| author_sort | Yakui Xue |
| collection | DOAJ |
| description | An epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below the capacity and is constant when the number of infective is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infective. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low. |
| format | Article |
| id | doaj-art-5c9a413ecacc46e88ddf5bed69adff89 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5c9a413ecacc46e88ddf5bed69adff892025-08-20T02:04:59ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/647853647853Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and TreatmentYakui Xue0Junfeng Wang1Department of Mathematics, North University of China, Shanxi Taiyuan 030051, ChinaDepartment of Mathematics, North University of China, Shanxi Taiyuan 030051, ChinaAn epidemic model with infectious force in infected and immune period and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infective on the disease spread. It is assumed that treatment rate is proportional to the number of infective below the capacity and is constant when the number of infective is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infective. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.http://dx.doi.org/10.1155/2012/647853 |
| spellingShingle | Yakui Xue Junfeng Wang Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment Abstract and Applied Analysis |
| title | Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment |
| title_full | Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment |
| title_fullStr | Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment |
| title_full_unstemmed | Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment |
| title_short | Backward Bifurcation of an Epidemic Model with Infectious Force in Infected and Immune Period and Treatment |
| title_sort | backward bifurcation of an epidemic model with infectious force in infected and immune period and treatment |
| url | http://dx.doi.org/10.1155/2012/647853 |
| work_keys_str_mv | AT yakuixue backwardbifurcationofanepidemicmodelwithinfectiousforceininfectedandimmuneperiodandtreatment AT junfengwang backwardbifurcationofanepidemicmodelwithinfectiousforceininfectedandimmuneperiodandtreatment |