Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense
In this work, a non-integer-order epidemic system modelling the nonlinear dynamics of Ebola virus disease is formulated in the sense of Caputo-ractional derivative. The existence and uniqueness of solution of the model is established. More importantly, the theoretical analysis carried out is aimed...
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Nigerian Society of Physical Sciences
2025-02-01
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| Series: | Journal of Nigerian Society of Physical Sciences |
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| Online Access: | https://journal.nsps.org.ng/index.php/jnsps/article/view/2304 |
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| author | Samson Olaniyi Furaha M. Chuma Sulaimon F. Abimbade |
| author_facet | Samson Olaniyi Furaha M. Chuma Sulaimon F. Abimbade |
| author_sort | Samson Olaniyi |
| collection | DOAJ |
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In this work, a non-integer-order epidemic system modelling the nonlinear dynamics of Ebola virus disease is formulated in the sense of Caputo-ractional derivative. The existence and uniqueness of solution of the model is established. More importantly, the theoretical analysis carried out is aimed at establishing the local and global asymptotic stability properties of the disease-free steady state of the epidemic model using the fractional Routh-Hurwitz criterion and Lyapunov functional technique, respectively. It is proved that the steady state is locally and globally asymptotically stable at the value of the key epidemiological threshold quantity lower than unity. The result is numerically validated for different values of fractional order to show the asymptotic behavior of the disease dynamics. This result is significant for fighting and preventing Ebola epidemic in the population, since the Caputo derivative operator allows for effective description of the disease dynamics with memory, where the future evolution of the disease is governed by its prior history.
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| format | Article |
| id | doaj-art-fe7feb7aa553404fb2a28b3645f7264c |
| institution | Kabale University |
| issn | 2714-2817 2714-4704 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Nigerian Society of Physical Sciences |
| record_format | Article |
| series | Journal of Nigerian Society of Physical Sciences |
| spelling | doaj-art-fe7feb7aa553404fb2a28b3645f7264c2025-01-17T18:52:27ZengNigerian Society of Physical SciencesJournal of Nigerian Society of Physical Sciences2714-28172714-47042025-02-017110.46481/jnsps.2025.2304Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo senseSamson Olaniyi0https://orcid.org/0000-0001-6492-1405Furaha M. Chuma1Sulaimon F. Abimbade2https://orcid.org/0000-0002-1992-9560Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, NigeriaDepartment of Physics, Mathematics and Informatics, Dar es Salaam University College of Education, TanzaniaDepartment of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria In this work, a non-integer-order epidemic system modelling the nonlinear dynamics of Ebola virus disease is formulated in the sense of Caputo-ractional derivative. The existence and uniqueness of solution of the model is established. More importantly, the theoretical analysis carried out is aimed at establishing the local and global asymptotic stability properties of the disease-free steady state of the epidemic model using the fractional Routh-Hurwitz criterion and Lyapunov functional technique, respectively. It is proved that the steady state is locally and globally asymptotically stable at the value of the key epidemiological threshold quantity lower than unity. The result is numerically validated for different values of fractional order to show the asymptotic behavior of the disease dynamics. This result is significant for fighting and preventing Ebola epidemic in the population, since the Caputo derivative operator allows for effective description of the disease dynamics with memory, where the future evolution of the disease is governed by its prior history. https://journal.nsps.org.ng/index.php/jnsps/article/view/2304Mathematical modelFractional orderCaputo derivative operatorEbola virus diseaseLyapunov stability |
| spellingShingle | Samson Olaniyi Furaha M. Chuma Sulaimon F. Abimbade Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense Journal of Nigerian Society of Physical Sciences Mathematical model Fractional order Caputo derivative operator Ebola virus disease Lyapunov stability |
| title | Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense |
| title_full | Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense |
| title_fullStr | Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense |
| title_full_unstemmed | Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense |
| title_short | Asymptotic stability analysis of a fractional epidemic model for Ebola virus disease in Caputo sense |
| title_sort | asymptotic stability analysis of a fractional epidemic model for ebola virus disease in caputo sense |
| topic | Mathematical model Fractional order Caputo derivative operator Ebola virus disease Lyapunov stability |
| url | https://journal.nsps.org.ng/index.php/jnsps/article/view/2304 |
| work_keys_str_mv | AT samsonolaniyi asymptoticstabilityanalysisofafractionalepidemicmodelforebolavirusdiseaseincaputosense AT furahamchuma asymptoticstabilityanalysisofafractionalepidemicmodelforebolavirusdiseaseincaputosense AT sulaimonfabimbade asymptoticstabilityanalysisofafractionalepidemicmodelforebolavirusdiseaseincaputosense |