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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 236352, 15 pages
Research Article

A Dengue Vaccination Model for Immigrants in a Two-Age-Class Population

1Department of Mathematics, Universitas Indonesia, Depok 16424, Indonesia
2Department of Mathematics, Universitas Padjadjaran, Jatinangor 45363, Indonesia
3Department of Mathematics, Institut Teknologi Bandung, Bandung 40132, Indonesia

Received 18 October 2011; Revised 2 January 2012; Accepted 17 February 2012

Academic Editor: A. Zayed

Copyright © 2012 Hengki Tasman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop a model of dengue transmission with some vaccination programs for immigrants. We classify the host population into child and adult classes, in regards to age structure, and into susceptible, infected and recovered compartments, in regards to disease status. Since migration plays important role in disease transmission, we include immigration and emigration factors into the model which are distributed in each compartment. Meanwhile, the vector population is divided into susceptible, exposed, and infectious compartments. In the case when there is no incoming infected immigrant, we obtain the basic reproduction ratio as a threshold parameter for existence and stability of disease-free and endemic equilibria. Meanwhile, in the case when there are some incoming infected immigrants, we obtain only endemic equilibrium. This indicates that screening for the immigrants is important to ensure the effectiveness of the disease control.