Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical Model
Coronavirus can be transmitted through the things that people carry or the things where it sticks to after being spread by the sufferer. Instead, various preventive measures have been carried out. We create a new mathematical model that represents Coronavirus that exists in non-living objects, susce...
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| Format: | Article |
| Language: | English |
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Akif AKGUL
2024-07-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3780420 |
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| author | Yuvita Andriani Kusumadewi Azimatus Nur Safitri Aulia Nurmalitasari Triyanto Triyanto Laila Fitriana Yudi Ari Adi Ario Wiraya |
| author_facet | Yuvita Andriani Kusumadewi Azimatus Nur Safitri Aulia Nurmalitasari Triyanto Triyanto Laila Fitriana Yudi Ari Adi Ario Wiraya |
| author_sort | Yuvita Andriani Kusumadewi |
| collection | DOAJ |
| description | Coronavirus can be transmitted through the things that people carry or the things where it sticks to after being spread by the sufferer. Instead, various preventive measures have been carried out. We create a new mathematical model that represents Coronavirus that exists in non-living objects, susceptible, and infected subpopulations interaction by considering the Coronavirus transmission through non-living objects caused by susceptible and infected subpopulations along with its prevention to characterize the dynamics of Coronavirus transmission in the population under those conditions. One disease-free and two infection equilibrium points along with their local stability and coexistence are identified. Global stability of the disease-free equilibria and basic reproduction number are also investigated. Changes in susceptible-Coronavirus interaction rate generate Fold and Hopf bifurcations which represent the emergence of a cycle and the collision of two infection equilibrium points respectively. Catastrophe generated by the collision between an attractor and a repeller is found around a Generalized Hopf bifurcation point by changing susceptible-Coronavirus interaction rate and increasing rate of Coronavirus originating from infected subpopulation. It represents a momentary unpredictable dynamics as the effect of Coronavirus addition and infection. Non-chaotic strange attractors that represent complex but still predictable dynamics are also triggered by Generalized Hopf bifurcation when the susceptible-Coronavirus interaction rate and one of the following parameters, i.e. increasing rate of Coronavirus originating from infected subpopulation or infected subpopulation recovery rate vary. |
| format | Article |
| id | doaj-art-ff88a6608e5d48b5b2d88fb344c441fb |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-ff88a6608e5d48b5b2d88fb344c441fb2025-01-23T18:19:34ZengAkif AKGULChaos Theory and Applications2687-45392024-07-016315916910.51537/chaos.14489121971Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical ModelYuvita Andriani Kusumadewihttps://orcid.org/0009-0005-8696-4402Azimatus Nur Safitrihttps://orcid.org/0009-0001-0819-1265Aulia Nurmalitasarihttps://orcid.org/0009-0001-7680-9338Triyanto Triyanto0https://orcid.org/0009-0009-6052-5339Laila Fitriana1https://orcid.org/0000-0002-1533-1617Yudi Ari Adi2https://orcid.org/0000-0002-1831-9103Ario Wiraya3https://orcid.org/0000-0002-1734-3419Universitas Sebelas MaretUniversitas Sebelas MaretUniversitas Ahmad DahlanUniversitas Sebelas MaretCoronavirus can be transmitted through the things that people carry or the things where it sticks to after being spread by the sufferer. Instead, various preventive measures have been carried out. We create a new mathematical model that represents Coronavirus that exists in non-living objects, susceptible, and infected subpopulations interaction by considering the Coronavirus transmission through non-living objects caused by susceptible and infected subpopulations along with its prevention to characterize the dynamics of Coronavirus transmission in the population under those conditions. One disease-free and two infection equilibrium points along with their local stability and coexistence are identified. Global stability of the disease-free equilibria and basic reproduction number are also investigated. Changes in susceptible-Coronavirus interaction rate generate Fold and Hopf bifurcations which represent the emergence of a cycle and the collision of two infection equilibrium points respectively. Catastrophe generated by the collision between an attractor and a repeller is found around a Generalized Hopf bifurcation point by changing susceptible-Coronavirus interaction rate and increasing rate of Coronavirus originating from infected subpopulation. It represents a momentary unpredictable dynamics as the effect of Coronavirus addition and infection. Non-chaotic strange attractors that represent complex but still predictable dynamics are also triggered by Generalized Hopf bifurcation when the susceptible-Coronavirus interaction rate and one of the following parameters, i.e. increasing rate of Coronavirus originating from infected subpopulation or infected subpopulation recovery rate vary.https://dergipark.org.tr/en/download/article-file/3780420covid-19catastrophegeneralized hopfstrange attractor |
| spellingShingle | Yuvita Andriani Kusumadewi Azimatus Nur Safitri Aulia Nurmalitasari Triyanto Triyanto Laila Fitriana Yudi Ari Adi Ario Wiraya Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical Model Chaos Theory and Applications covid-19 catastrophe generalized hopf strange attractor |
| title | Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical Model |
| title_full | Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical Model |
| title_fullStr | Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical Model |
| title_full_unstemmed | Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical Model |
| title_short | Birth of Catastrophe and Strange Attractors through Generalized Hopf Bifurcations in Covid-19 Transmission Mathematical Model |
| title_sort | birth of catastrophe and strange attractors through generalized hopf bifurcations in covid 19 transmission mathematical model |
| topic | covid-19 catastrophe generalized hopf strange attractor |
| url | https://dergipark.org.tr/en/download/article-file/3780420 |
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