Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays
This study focuses on a mathematical model of Zika virus transmission that incorporates multiple time delays. The inclusion of time delays in the model takes into account the incubation period in humans and the latency of disease transmission from mosquitoes. The qualitative behavior of the model wa...
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| Format: | Article |
| Language: | English |
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Mahmut Akyigit
2025-03-01
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| Series: | Journal of Mathematical Sciences and Modelling |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4466212 |
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| _version_ | 1850174011826241536 |
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| author | Müge Meyvacı |
| author_facet | Müge Meyvacı |
| author_sort | Müge Meyvacı |
| collection | DOAJ |
| description | This study focuses on a mathematical model of Zika virus transmission that incorporates multiple time delays. The inclusion of time delays in the model takes into account the incubation period in humans and the latency of disease transmission from mosquitoes. The qualitative behavior of the model was examined in four different conditions by analyzing the characteristic equation corresponding to the endemic equilibrium point. Furthermore, the two distinct time lags were selected as the bifurcation parameter, while the existence of a Hopf bifurcation at the endemic equilibrium point for threshold parameters was confirmed. Subsequently, numerical simulations were used to validate the theoretical analysis for each case using MATLAB. |
| format | Article |
| id | doaj-art-99d32f43ccfa45c09fce48e447bcf74a |
| institution | OA Journals |
| issn | 2636-8692 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj-art-99d32f43ccfa45c09fce48e447bcf74a2025-08-20T02:19:44ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922025-03-0181132110.33187/jmsm.16071131408Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time DelaysMüge Meyvacı0https://orcid.org/0000-0002-4772-3869MIMAR SINAN FINE ARTS UNIVERSITYThis study focuses on a mathematical model of Zika virus transmission that incorporates multiple time delays. The inclusion of time delays in the model takes into account the incubation period in humans and the latency of disease transmission from mosquitoes. The qualitative behavior of the model was examined in four different conditions by analyzing the characteristic equation corresponding to the endemic equilibrium point. Furthermore, the two distinct time lags were selected as the bifurcation parameter, while the existence of a Hopf bifurcation at the endemic equilibrium point for threshold parameters was confirmed. Subsequently, numerical simulations were used to validate the theoretical analysis for each case using MATLAB.https://dergipark.org.tr/en/download/article-file/4466212bifurcationhopf bifurcationstability |
| spellingShingle | Müge Meyvacı Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays Journal of Mathematical Sciences and Modelling bifurcation hopf bifurcation stability |
| title | Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays |
| title_full | Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays |
| title_fullStr | Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays |
| title_full_unstemmed | Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays |
| title_short | Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays |
| title_sort | hopf bifurcation analysis of a zika virus transmission model with two time delays |
| topic | bifurcation hopf bifurcation stability |
| url | https://dergipark.org.tr/en/download/article-file/4466212 |
| work_keys_str_mv | AT mugemeyvacı hopfbifurcationanalysisofazikavirustransmissionmodelwithtwotimedelays |