Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers
In this paper, an epidemic model is investigated for infectious diseases that can be transmitted through both the infectious individuals and the asymptomatic carriers (i.e., infected individuals who are contagious but do not show any disease symptoms). We propose a dose-structured vaccination model...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016019 |
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| author | Martin Luther Mann Manyombe Joseph Mbang Jean Lubuma Berge Tsanou |
| author_facet | Martin Luther Mann Manyombe Joseph Mbang Jean Lubuma Berge Tsanou |
| author_sort | Martin Luther Mann Manyombe |
| collection | DOAJ |
| description | In this paper, an epidemic model is investigated for infectious diseases that can be transmitted through both the infectious individuals and the asymptomatic carriers (i.e., infected individuals who are contagious but do not show any disease symptoms). We propose a dose-structured vaccination model with multiple transmission pathways. Based on the range of the explicitly computed basic reproduction number, we prove the global stability of the disease-free when this threshold number is less or equal to the unity. Moreover, whenever it is greater than one, the existence of the unique endemic equilibrium is shown and its global stability is established for the case where the changes of displaying the disease symptoms are independent of the vulnerable classes. Further, the model is shown to exhibit a transcritical bifurcation with the unit basic reproduction number being the bifurcation parameter. The impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission are discussed through through the local and the global sensitivity analyses of the basic reproduction number. Finally, a case study of hepatitis B virus disease (HBV) is considered, with the numerical simulations presented to support the analytical results. They further suggest that, in high HBV prevalence countries, the combination of effective vaccination (i.e. $\geq 3$ doses of HepB vaccine), the diagnosis of asymptomatic carriers and the treatment of symptomatic carriers may have a much greater positive impact on the disease control. |
| format | Article |
| id | doaj-art-eab9bb486d234c739049ff16db5ec96d |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-eab9bb486d234c739049ff16db5ec96d2025-01-24T02:36:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-04-0113481384010.3934/mbe.2016019Global dynamics of a vaccination model for infectious diseases with asymptomatic carriersMartin Luther Mann Manyombe0Joseph Mbang1Jean Lubuma2Berge Tsanou3Department of Mathematics, Faculty of Science, University of Yaounde 1, P.O. Box 812 YaoundeDepartment of Mathematics, Faculty of Science, University of Yaounde 1, P.O. Box 812 YaoundeDepartment of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002In this paper, an epidemic model is investigated for infectious diseases that can be transmitted through both the infectious individuals and the asymptomatic carriers (i.e., infected individuals who are contagious but do not show any disease symptoms). We propose a dose-structured vaccination model with multiple transmission pathways. Based on the range of the explicitly computed basic reproduction number, we prove the global stability of the disease-free when this threshold number is less or equal to the unity. Moreover, whenever it is greater than one, the existence of the unique endemic equilibrium is shown and its global stability is established for the case where the changes of displaying the disease symptoms are independent of the vulnerable classes. Further, the model is shown to exhibit a transcritical bifurcation with the unit basic reproduction number being the bifurcation parameter. The impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission are discussed through through the local and the global sensitivity analyses of the basic reproduction number. Finally, a case study of hepatitis B virus disease (HBV) is considered, with the numerical simulations presented to support the analytical results. They further suggest that, in high HBV prevalence countries, the combination of effective vaccination (i.e. $\geq 3$ doses of HepB vaccine), the diagnosis of asymptomatic carriers and the treatment of symptomatic carriers may have a much greater positive impact on the disease control.https://www.aimspress.com/article/doi/10.3934/mbe.2016019asymptomatic carriershbv infection.lyapunovstabilityforward bifurcationeffectiveness of vaccination |
| spellingShingle | Martin Luther Mann Manyombe Joseph Mbang Jean Lubuma Berge Tsanou Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers Mathematical Biosciences and Engineering asymptomatic carriers hbv infection. lyapunov stability forward bifurcation effectiveness of vaccination |
| title | Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers |
| title_full | Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers |
| title_fullStr | Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers |
| title_full_unstemmed | Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers |
| title_short | Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers |
| title_sort | global dynamics of a vaccination model for infectious diseases with asymptomatic carriers |
| topic | asymptomatic carriers hbv infection. lyapunov stability forward bifurcation effectiveness of vaccination |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016019 |
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