Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model
We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/434537 |
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| _version_ | 1832563427266002944 |
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| author | Zhijian Wei Meitao Le |
| author_facet | Zhijian Wei Meitao Le |
| author_sort | Zhijian Wei |
| collection | DOAJ |
| description | We consider a class of system of nonlinear difference
equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known results. |
| format | Article |
| id | doaj-art-4eb92fbbb124430199c01c8635a0f612 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4eb92fbbb124430199c01c8635a0f6122025-02-03T01:20:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/434537434537Existence and Convergence of the Positive Solutions of a Discrete Epidemic ModelZhijian Wei0Meitao Le1College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, ChinaCollege of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, ChinaWe consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known results.http://dx.doi.org/10.1155/2015/434537 |
| spellingShingle | Zhijian Wei Meitao Le Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model Discrete Dynamics in Nature and Society |
| title | Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model |
| title_full | Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model |
| title_fullStr | Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model |
| title_full_unstemmed | Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model |
| title_short | Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model |
| title_sort | existence and convergence of the positive solutions of a discrete epidemic model |
| url | http://dx.doi.org/10.1155/2015/434537 |
| work_keys_str_mv | AT zhijianwei existenceandconvergenceofthepositivesolutionsofadiscreteepidemicmodel AT meitaole existenceandconvergenceofthepositivesolutionsofadiscreteepidemicmodel |