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Journal of Applied Mathematics
Volume 2018 (2018), Article ID 9674138, 13 pages
https://doi.org/10.1155/2018/9674138
Research Article

Understanding Dengue Control for Short- and Long-Term Intervention with a Mathematical Model Approach

Department of Mathematics, Universitas Indonesia, Depok 16424, Indonesia

Correspondence should be addressed to D. Aldila; di.ca.iu.ics@opidalidla

Received 10 August 2017; Accepted 19 November 2017; Published 1 January 2018

Academic Editor: Lucas Jodar

Copyright © 2018 A. Bustamam 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.

Abstract

A mathematical model of dengue diseases transmission will be discussed in this paper. Various interventions, such as vaccination of adults and newborns, the use of insecticides or fumigation, and also the enforcement of mechanical controls, will be considered when analyzing the best intervention for controlling the spread of dengue. From model analysis, we find three types of equilibrium points which will be built upon the dengue model. In this paper, these points are the mosquito-free equilibrium, disease-free equilibrium (with and without vaccinated compartment), and endemic equilibrium. Basic reproduction number as an endemic indicator has been found analytically. Based on analytical and numerical analysis, insecticide treatment, adult vaccine, and enforcement of mechanical control are the most significant interventions in reducing the spread of dengue disease infection caused by mosquitoes rather than larvicide treatment and vaccination of newborns. From short- and long-term simulation, we find that insecticide treatment is the best strategy to control dengue. We also find that, with periodic intervention, the result is not much significantly different with constant intervention based on reduced number of the infected human population. Therefore, with budget limitations, periodic intervention of insecticide strategy is a good alternative to reduce the spread of dengue.