Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection
A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied.The condition for the global stability of the disease free equilibrium is obtained.The existence of the endemic equilibrium and its stability are investigated.More attention is paid to...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1399 |
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| _version_ | 1832590122038591488 |
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| author | Hui Cao Yicang Zhou Zhien Ma |
| author_facet | Hui Cao Yicang Zhou Zhien Ma |
| author_sort | Hui Cao |
| collection | DOAJ |
| description | A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied.The condition for the global stability of the disease free equilibrium is obtained.The existence of the endemic equilibrium and its stability are investigated.More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation.Sufficient conditions for those bifurcations have been obtained.Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model. |
| format | Article |
| id | doaj-art-6c75df71e3b94ea29c77ab909e5ca8b1 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-6c75df71e3b94ea29c77ab909e5ca8b12025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61399141710.3934/mbe.2013.10.1399Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infectionHui Cao0Yicang Zhou1Zhien Ma2Department of Mathematics, Shaanxi University of Science & Technology, Xi'an, 710021Department of Mathematics, Xi'an Jiaotong University, Xi'an, 710049Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied.The condition for the global stability of the disease free equilibrium is obtained.The existence of the endemic equilibrium and its stability are investigated.More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation.Sufficient conditions for those bifurcations have been obtained.Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1399hopf bifurcation.bilinear incidenceflip bifurcationsaddle-node bifurcationdiscrete sis model |
| spellingShingle | Hui Cao Yicang Zhou Zhien Ma Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection Mathematical Biosciences and Engineering hopf bifurcation. bilinear incidence flip bifurcation saddle-node bifurcation discrete sis model |
| title | Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection |
| title_full | Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection |
| title_fullStr | Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection |
| title_full_unstemmed | Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection |
| title_short | Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection |
| title_sort | bifurcation analysis of a discrete sis model with bilinear incidence depending on new infection |
| topic | hopf bifurcation. bilinear incidence flip bifurcation saddle-node bifurcation discrete sis model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1399 |
| work_keys_str_mv | AT huicao bifurcationanalysisofadiscretesismodelwithbilinearincidencedependingonnewinfection AT yicangzhou bifurcationanalysisofadiscretesismodelwithbilinearincidencedependingonnewinfection AT zhienma bifurcationanalysisofadiscretesismodelwithbilinearincidencedependingonnewinfection |