A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination
In this study, we proposed a fractional order model of hepatitis B virus transmission dynamics with two-age structure under vaccination. A qualitative analysis of the model is performed. Basic reproduction number of the model is determined. Local stability conditions of disease-free equilibrium poin...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2021-01-01
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| Series: | Arab Journal of Basic and Applied Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/25765299.2021.1896423 |
| _version_ | 1818966857486434304 |
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| author | Getachew Teshome Tilahun Woldegebriel Assefa Woldegerima Nesredin Mohammed |
| author_facet | Getachew Teshome Tilahun Woldegebriel Assefa Woldegerima Nesredin Mohammed |
| author_sort | Getachew Teshome Tilahun |
| collection | DOAJ |
| description | In this study, we proposed a fractional order model of hepatitis B virus transmission dynamics with two-age structure under vaccination. A qualitative analysis of the model is performed. Basic reproduction number of the model is determined. Local stability conditions of disease-free equilibrium point are proven by using fractional Ruth-Hurwitz conditions. Global stability conditions of both disease-free and endemic equilibrium points are shown by constructing appropriate Lyapunov functions. Sensitivity analysis was done by using normalized forward sensitivity index approach. Numerical simulation is performed to investigate the effect of memory on hepatitis B disease dynamics by varying order of derivatives and to simulate the effects of vaccinating newborns immediately after birth, vaccinating children and adult vaccination. Then, we compared their effects on hepatitis B disease dynamics in the sense of control and elimination. It is observed that the number of infective individuals decreases faster and even falls to zero over a long run for the model with memory than memory-less model. Comparing results between vaccination of different ages show that increasing newborn vaccination immediately after birth has the highest effect on hepatitis B disease control. |
| first_indexed | 2024-12-20T13:39:34Z |
| format | Article |
| id | doaj.art-ea4eae2e388e4275af0f014035177cea |
| institution | Directory Open Access Journal |
| issn | 2576-5299 |
| language | English |
| last_indexed | 2024-12-20T13:39:34Z |
| publishDate | 2021-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj.art-ea4eae2e388e4275af0f014035177cea2022-12-21T19:38:50ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992021-01-012818710610.1080/25765299.2021.18964231896423A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccinationGetachew Teshome Tilahun0Woldegebriel Assefa Woldegerima1Nesredin Mohammed2Department of Mathematics, CNCS, Haramaya UniversityDepartment of Mathematics and Applied Mathematics, University of PretoriaDepartment of Mathematics, CNCS, Haramaya UniversityIn this study, we proposed a fractional order model of hepatitis B virus transmission dynamics with two-age structure under vaccination. A qualitative analysis of the model is performed. Basic reproduction number of the model is determined. Local stability conditions of disease-free equilibrium point are proven by using fractional Ruth-Hurwitz conditions. Global stability conditions of both disease-free and endemic equilibrium points are shown by constructing appropriate Lyapunov functions. Sensitivity analysis was done by using normalized forward sensitivity index approach. Numerical simulation is performed to investigate the effect of memory on hepatitis B disease dynamics by varying order of derivatives and to simulate the effects of vaccinating newborns immediately after birth, vaccinating children and adult vaccination. Then, we compared their effects on hepatitis B disease dynamics in the sense of control and elimination. It is observed that the number of infective individuals decreases faster and even falls to zero over a long run for the model with memory than memory-less model. Comparing results between vaccination of different ages show that increasing newborn vaccination immediately after birth has the highest effect on hepatitis B disease control.http://dx.doi.org/10.1080/25765299.2021.1896423hepatitis b virusmemoryfractional orderage structuremathematical modelvaccinationbasic reproduction number |
| spellingShingle | Getachew Teshome Tilahun Woldegebriel Assefa Woldegerima Nesredin Mohammed A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination Arab Journal of Basic and Applied Sciences hepatitis b virus memory fractional order age structure mathematical model vaccination basic reproduction number |
| title | A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination |
| title_full | A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination |
| title_fullStr | A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination |
| title_full_unstemmed | A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination |
| title_short | A fractional order model for the transmission dynamics of hepatitis B virus with two-age structure in the presence of vaccination |
| title_sort | fractional order model for the transmission dynamics of hepatitis b virus with two age structure in the presence of vaccination |
| topic | hepatitis b virus memory fractional order age structure mathematical model vaccination basic reproduction number |
| url | http://dx.doi.org/10.1080/25765299.2021.1896423 |
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