Complex Dynamics of Discrete SEIS Models with Simple Demography
We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/653937 |
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| _version_ | 1850228575597232128 |
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| author | Hui Cao Yicang Zhou Baojun Song |
| author_facet | Hui Cao Yicang Zhou Baojun Song |
| author_sort | Hui Cao |
| collection | DOAJ |
| description | We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorously mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals. |
| format | Article |
| id | doaj-art-2b68b1c406f04f0ea322f91c3368a2fa |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-2b68b1c406f04f0ea322f91c3368a2fa2025-08-20T02:04:30ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/653937653937Complex Dynamics of Discrete SEIS Models with Simple DemographyHui Cao0Yicang Zhou1Baojun Song2Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, ChinaDepartment of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, ChinaDepartment of Mathematical Sciences, Montclair State University, Montclair, NJ 07043, USAWe investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorously mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals.http://dx.doi.org/10.1155/2011/653937 |
| spellingShingle | Hui Cao Yicang Zhou Baojun Song Complex Dynamics of Discrete SEIS Models with Simple Demography Discrete Dynamics in Nature and Society |
| title | Complex Dynamics of Discrete SEIS Models with Simple Demography |
| title_full | Complex Dynamics of Discrete SEIS Models with Simple Demography |
| title_fullStr | Complex Dynamics of Discrete SEIS Models with Simple Demography |
| title_full_unstemmed | Complex Dynamics of Discrete SEIS Models with Simple Demography |
| title_short | Complex Dynamics of Discrete SEIS Models with Simple Demography |
| title_sort | complex dynamics of discrete seis models with simple demography |
| url | http://dx.doi.org/10.1155/2011/653937 |
| work_keys_str_mv | AT huicao complexdynamicsofdiscreteseismodelswithsimpledemography AT yicangzhou complexdynamicsofdiscreteseismodelswithsimpledemography AT baojunsong complexdynamicsofdiscreteseismodelswithsimpledemography |