Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate
This paper is concerned with a delayed SEIS (Susceptible-Exposed-Infectious-Susceptible) epidemic model with a changing delitescence and nonlinear incidence rate. First of all, local stability of the endemic equilibrium and the existence of a Hopf bifurcation are studied by choosing the time delay a...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/2340549 |
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| _version_ | 1832563018973577216 |
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| author | Juan Liu |
| author_facet | Juan Liu |
| author_sort | Juan Liu |
| collection | DOAJ |
| description | This paper is concerned with a delayed SEIS (Susceptible-Exposed-Infectious-Susceptible) epidemic model with a changing delitescence and nonlinear incidence rate. First of all, local stability of the endemic equilibrium and the existence of a Hopf bifurcation are studied by choosing the time delay as the bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are determined based on the normal form theory and the center manifold theorem. At last, numerical simulations are carried out to illustrate the obtained theoretical results. |
| format | Article |
| id | doaj-art-640edf1c360e44cfbf66071c3c759b62 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-640edf1c360e44cfbf66071c3c759b622025-02-03T01:21:07ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/23405492340549Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence RateJuan Liu0Department of Mathematics and Physics, Bengbu University, Bengbu 233030, ChinaThis paper is concerned with a delayed SEIS (Susceptible-Exposed-Infectious-Susceptible) epidemic model with a changing delitescence and nonlinear incidence rate. First of all, local stability of the endemic equilibrium and the existence of a Hopf bifurcation are studied by choosing the time delay as the bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are determined based on the normal form theory and the center manifold theorem. At last, numerical simulations are carried out to illustrate the obtained theoretical results.http://dx.doi.org/10.1155/2017/2340549 |
| spellingShingle | Juan Liu Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate Discrete Dynamics in Nature and Society |
| title | Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate |
| title_full | Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate |
| title_fullStr | Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate |
| title_full_unstemmed | Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate |
| title_short | Bifurcation of a Delayed SEIS Epidemic Model with a Changing Delitescence and Nonlinear Incidence Rate |
| title_sort | bifurcation of a delayed seis epidemic model with a changing delitescence and nonlinear incidence rate |
| url | http://dx.doi.org/10.1155/2017/2340549 |
| work_keys_str_mv | AT juanliu bifurcationofadelayedseisepidemicmodelwithachangingdelitescenceandnonlinearincidencerate |