A two-age-classes dengue transmission model |
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Authors: | Supriatna A K Soewono E van Gils S A |
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Institution: | a Department of Mathematics, Universitas Padjadjaran, Jl. Raya Bandung-Sumedang Km 21, Jatinangor, Sumedang, West Java 45363, Indonesia b Industrial and Financial Mathematics Group, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia c Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands |
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Abstract: | In this paper, we discuss a two-age-classes dengue transmission model with vaccination. The reason to divide the human population into two age classes is for practical purpose, as vaccination is usually concentrated in one age class. We assume that a constant rate of individuals in the child-class is vaccinated. We analyze a threshold number which is equivalent to the basic reproduction number. If there is an undeliberate vaccination to infectious children, which worsens their condition as the time span of being infectious increases, then paradoxically, vaccination can be counter productive. The paradox, stating that vaccination makes the basic reproduction number even bigger, can occur if the worsening effect is greater than a certain threshold, a function of the human demographic and epidemiological parameters, which is independent of the level of vaccination. However, if the worsening effect is to increase virulence so that one will develop symptoms, then the vaccination is always productive. In both situations, screening should take place before vaccination. In general, the presence of class division has obscured the known rule of thumb for vaccination. |
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Keywords: | Dengue transmission model Basic reproduction number Critical vaccination level |
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