Epidemic models with nonlinear infection forces
Epidemic models with behavior changes are studied to consider effects of protection measures and intervention policies. It is found that intervention strategies decrease endemic levels and tend to make the dynamical behavior of a disease evolution simpler. For a saturated infection force, the model...
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| Format: | Article |
| Language: | English |
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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.2006.3.267 |
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| _version_ | 1832590261092352000 |
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| author | Wendi Wang |
| author_facet | Wendi Wang |
| author_sort | Wendi Wang |
| collection | DOAJ |
| description | Epidemic models with behavior changes are studied to consider effects of protection measures and intervention policies. It is found that intervention strategies decrease endemic levels and tend to make the dynamical behavior of a disease evolution simpler. For a saturated infection force, the model may admit a stable disease-free equilibrium and a stable endemic equilibrium at the same time. If we vary a recovery rate, numerical simulations show that the boundaries of the region for the persistence of the disease undergo the changes from the separatrix of a saddle to an unstable limit cycle. If the inhibition effect from behavior changes is weak, we find two limit cycles and obtain bifurcations of the model as the population size changes. We also find that the disease may die out although there are two endemic equilibria. |
| format | Article |
| id | doaj-art-6f7f9c55e8ac4005b3732be7488c688c |
| 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-6f7f9c55e8ac4005b3732be7488c688c2025-01-24T01:51:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-10-013126727910.3934/mbe.2006.3.267Epidemic models with nonlinear infection forcesWendi Wang0Department of Mathematics, Southwest Normal University, Chongqing, 400715, PREpidemic models with behavior changes are studied to consider effects of protection measures and intervention policies. It is found that intervention strategies decrease endemic levels and tend to make the dynamical behavior of a disease evolution simpler. For a saturated infection force, the model may admit a stable disease-free equilibrium and a stable endemic equilibrium at the same time. If we vary a recovery rate, numerical simulations show that the boundaries of the region for the persistence of the disease undergo the changes from the separatrix of a saddle to an unstable limit cycle. If the inhibition effect from behavior changes is weak, we find two limit cycles and obtain bifurcations of the model as the population size changes. We also find that the disease may die out although there are two endemic equilibria.https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.267basic reproduction numberepidemiccycles.stabilitynonlinear incidence |
| spellingShingle | Wendi Wang Epidemic models with nonlinear infection forces Mathematical Biosciences and Engineering basic reproduction number epidemic cycles. stability nonlinear incidence |
| title | Epidemic models with nonlinear infection forces |
| title_full | Epidemic models with nonlinear infection forces |
| title_fullStr | Epidemic models with nonlinear infection forces |
| title_full_unstemmed | Epidemic models with nonlinear infection forces |
| title_short | Epidemic models with nonlinear infection forces |
| title_sort | epidemic models with nonlinear infection forces |
| topic | basic reproduction number epidemic cycles. stability nonlinear incidence |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2006.3.267 |
| work_keys_str_mv | AT wendiwang epidemicmodelswithnonlinearinfectionforces |