Numerical analysis of the SIR-SI differential equations with application to dengue disease mapping in Kuala Lumpur, Malaysia

Samat, NA; Percy, DF

Abstract

The main aim of this study is to describe and introduce a method of numerical analysis in obtaining approximate solutions for the SIR-SI differential equations (susceptible-infective-recovered for human populations; susceptible-infective for vector populations) that represent a model for dengue disease transmission. Firstly, we describe the ordinary differential equations for the SIR-SI disease transmission models. Then, we introduce the numerical analysis of solutions of this continuous time, discrete space SIR-SI model by simplifying the continuous time scale to a densely populated, discrete time scale. This is followed by the application of this numerical analysis of solutions of the SIR-SI differential equations to the estimation of relative risk using continuous time, discrete space dengue data of Kuala Lumpur, Malaysia. Finally, we present the results of the analysis, comparing and displaying the results in graphs, table and maps. Results of the numerical analysis of solutions that we implemented offers a useful and potentially superior model for estimating relative risks based on continuous time, discrete space data for vector borne infectious diseases specifically for dengue disease.

Citation

Samat, N., & Percy, D. (2013). Numerical analysis of the SIR-SI differential equations with application to dengue disease mapping in Kuala Lumpur, Malaysia

• Journal Article Type: Article
• Publication Date: Jan 1, 2013
• Deposit Date: Aug 15, 2015
• Journal: International Journal of Mathematical, Computational, Statistical, Natural and Physical Engineering
• Peer Reviewed: Peer Reviewed
• Volume: 7
• Pages: 642-651
• Publisher URL: https://www.waset.org/journal/Mathematical
• Additional Information: Funders : Universiti Pendidikan Sultan Idris and the Ministry of Higher Education in Malaysia