Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate
We study an epidemic model with a nonlinear incidence rate which describes the psychological effect of certain serious diseases on the community when the ratio of the number of infectives to that of the susceptibles is getting larger. The model has set up a challenging issue regarding its dynamics n...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/609306 |
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| _version_ | 1832563125882191872 |
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| author | Sanling Yuan Bo Li |
| author_facet | Sanling Yuan Bo Li |
| author_sort | Sanling Yuan |
| collection | DOAJ |
| description | We study an epidemic model with a nonlinear incidence rate which
describes the psychological effect of certain serious diseases on the community when the ratio
of the number of infectives to that of the susceptibles is getting larger. The model has set up
a challenging issue regarding its dynamics near the origin since it is not well defined there.
By carrying out a global analysis of the model and studying the stabilities of the disease-free equilibrium and the endemic equilibrium, it is shown that either the number of infective
individuals tends to zero as time evolves or the disease persists. Computer simulations are
presented to illustrate the results. |
| format | Article |
| id | doaj-art-fc8a9fdcc5e24574ab38afe871adbdd9 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-fc8a9fdcc5e24574ab38afe871adbdd92025-02-03T01:21:00ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/609306609306Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence RateSanling Yuan0Bo Li1College of Science, Shanghai University for Science and Technology, Shanghai 200093, ChinaCollege of Science, Shanghai University for Science and Technology, Shanghai 200093, ChinaWe study an epidemic model with a nonlinear incidence rate which describes the psychological effect of certain serious diseases on the community when the ratio of the number of infectives to that of the susceptibles is getting larger. The model has set up a challenging issue regarding its dynamics near the origin since it is not well defined there. By carrying out a global analysis of the model and studying the stabilities of the disease-free equilibrium and the endemic equilibrium, it is shown that either the number of infective individuals tends to zero as time evolves or the disease persists. Computer simulations are presented to illustrate the results.http://dx.doi.org/10.1155/2009/609306 |
| spellingShingle | Sanling Yuan Bo Li Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate Discrete Dynamics in Nature and Society |
| title | Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate |
| title_full | Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate |
| title_fullStr | Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate |
| title_full_unstemmed | Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate |
| title_short | Global Dynamics of an Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate |
| title_sort | global dynamics of an epidemic model with a ratio dependent nonlinear incidence rate |
| url | http://dx.doi.org/10.1155/2009/609306 |
| work_keys_str_mv | AT sanlingyuan globaldynamicsofanepidemicmodelwitharatiodependentnonlinearincidencerate AT boli globaldynamicsofanepidemicmodelwitharatiodependentnonlinearincidencerate |