Competing species models with an infectious disease
The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number $\mathbf{R}_1$ determin...
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AIMS Press
2005-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.219 |
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| author | Roberto A. Saenz Herbert W. Hethcote |
| author_facet | Roberto A. Saenz Herbert W. Hethcote |
| author_sort | Roberto A. Saenz |
| collection | DOAJ |
| description | The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number $\mathbf{R}_1$ determines the asymptotic behavior, so that the disease dies out if $\mathbf{R}_1 \leq 1$ and approaches a globally attractive endemic equilibrium if $\mathbf{R}_1 > 1$. Because the disease- reduced reproduction and disease-related death rates are often different in two competing species, a shared disease can change the outcome of the competition. Models of SIR and SIRS type are also considered. A key result in all of these models with the frequency-dependent incidence is that the disease must either die out in both species or remain endemic in both species. |
| format | Article |
| id | doaj-art-f0e4f1450fff4595943f059f399dc72c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f0e4f1450fff4595943f059f399dc72c2025-01-24T01:51:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-013121923510.3934/mbe.2006.3.219Competing species models with an infectious diseaseRoberto A. Saenz0Herbert W. Hethcote1Applied Mathematical and Computational Sciences, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242Applied Mathematical and Computational Sciences, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242The frequency-dependent (standard) form of the incidence is used for the transmission dynamics of an infectious disease in a competing species model. In the global analysis of the SIS model with the birth rate independent of the population size, a modified reproduction number $\mathbf{R}_1$ determines the asymptotic behavior, so that the disease dies out if $\mathbf{R}_1 \leq 1$ and approaches a globally attractive endemic equilibrium if $\mathbf{R}_1 > 1$. Because the disease- reduced reproduction and disease-related death rates are often different in two competing species, a shared disease can change the outcome of the competition. Models of SIR and SIRS type are also considered. A key result in all of these models with the frequency-dependent incidence is that the disease must either die out in both species or remain endemic in both species.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.219coexistencemathematical modelsepidemiologydynamicscompeting speciesecologyinfectious diseasereproduction number. |
| spellingShingle | Roberto A. Saenz Herbert W. Hethcote Competing species models with an infectious disease Mathematical Biosciences and Engineering coexistence mathematical models epidemiology dynamics competing species ecology infectious disease reproduction number. |
| title | Competing species models with an infectious disease |
| title_full | Competing species models with an infectious disease |
| title_fullStr | Competing species models with an infectious disease |
| title_full_unstemmed | Competing species models with an infectious disease |
| title_short | Competing species models with an infectious disease |
| title_sort | competing species models with an infectious disease |
| topic | coexistence mathematical models epidemiology dynamics competing species ecology infectious disease reproduction number. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.219 |
| work_keys_str_mv | AT robertoasaenz competingspeciesmodelswithaninfectiousdisease AT herbertwhethcote competingspeciesmodelswithaninfectiousdisease |