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Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

1. Department of Mathematics, Faculty of Science, University of Yaounde 1, P.O. Box 812 Yaounde
2. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002

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.
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Keywords Asymptomatic carriers; HBV infection.; Lyapunov; stability; forward bifurcation; effectiveness of vaccination

Citation: 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, 2016, 13(4): 813-840. doi: 10.3934/mbe.2016019

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  • 3. Leontine Nkague Nkamba, Thomas Timothee Manga, Franklin Agouanet, Martin Luther Mann Manyombe, Mathematical model to assess vaccination and effective contact rate impact in the spread of tuberculosis, Journal of Biological Dynamics, 2019, 13, 1, 26, 10.1080/17513758.2018.1563218

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Copyright Info: 2016, Martin Luther Mann Manyombe, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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