Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model
This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2018-01-01
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| Series: | Journal of Biological Dynamics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/17513758.2017.1401676 |
| _version_ | 1818233276103393280 |
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| author | Michael Barfield Maia Martcheva Necibe Tuncer Robert D. Holt |
| author_facet | Michael Barfield Maia Martcheva Necibe Tuncer Robert D. Holt |
| author_sort | Michael Barfield |
| collection | DOAJ |
| description | This paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model. The ODE model exhibits backward bifurcation and sustained oscillations caused by the stress-induced competition. Furthermore, the ODE model, although not a special case of the PDE model, is useful for detecting backward bifurcation and oscillations in the PDE model. Backward bifurcation related to stress-induced competition allows the second species to persist for values of its invasion number below one. Furthermore, stress-induced competition leads to destabilization of the coexistence equilibrium and sustained oscillations in the PDE model. We suggest that complex systems such as this one may be studied by appropriately designed simple ODE models. |
| first_indexed | 2024-12-12T11:19:36Z |
| format | Article |
| id | doaj.art-5251308b92164406ade4ce4a08990cda |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-12-12T11:19:36Z |
| publishDate | 2018-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-5251308b92164406ade4ce4a08990cda2022-12-22T00:26:03ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662018-01-01121518810.1080/17513758.2017.14016761401676Backward bifurcation and oscillations in a nested immuno-eco-epidemiological modelMichael Barfield0Maia Martcheva1Necibe Tuncer2Robert D. Holt3University of FloridaUniversity of FloridaFlorida Atlantic UniversityUniversity of FloridaThis paper introduces a novel partial differential equation immuno-eco-epidemiological model of competition in which one species is affected by a disease while another can compete with it directly and by lowering the first species' immune response to the infection, a mode of competition termed stress-induced competition. When the disease is chronic, and the within-host dynamics are rapid, we reduce the partial differential equation model (PDE) to a three-dimensional ordinary differential equation (ODE) model. The ODE model exhibits backward bifurcation and sustained oscillations caused by the stress-induced competition. Furthermore, the ODE model, although not a special case of the PDE model, is useful for detecting backward bifurcation and oscillations in the PDE model. Backward bifurcation related to stress-induced competition allows the second species to persist for values of its invasion number below one. Furthermore, stress-induced competition leads to destabilization of the coexistence equilibrium and sustained oscillations in the PDE model. We suggest that complex systems such as this one may be studied by appropriately designed simple ODE models.http://dx.doi.org/10.1080/17513758.2017.1401676backward bifurcationmulti-scale modelsoscillationsimmuno-eco-epi modelstress-induced competitioninfectious disease ecology |
| spellingShingle | Michael Barfield Maia Martcheva Necibe Tuncer Robert D. Holt Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model Journal of Biological Dynamics backward bifurcation multi-scale models oscillations immuno-eco-epi model stress-induced competition infectious disease ecology |
| title | Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model |
| title_full | Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model |
| title_fullStr | Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model |
| title_full_unstemmed | Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model |
| title_short | Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model |
| title_sort | backward bifurcation and oscillations in a nested immuno eco epidemiological model |
| topic | backward bifurcation multi-scale models oscillations immuno-eco-epi model stress-induced competition infectious disease ecology |
| url | http://dx.doi.org/10.1080/17513758.2017.1401676 |
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