Numerical Analysis of the SIR-SI Differential Equations with Application to Dengue Disease Mapping in Kuala Lumpur, Malaysia
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-infectiverecovered 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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1086991Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2343
 H. Nishiura, Mathematical and statistical analysis of the spread of dengue, Dengue Bulletin, vol. 30, pp. 51-67, 2006.
 L. Bernardinelli, D. G. Clayton, C. Pascutto, C. Montomoli, M. Ghislandi and M. Songini, Bayesian analysis of space-time variation in disease risk, Statistics in Medicine, vol. 14, pp. 2433-2443, 1995.
 N. A. Samat and D. F. Percy, Vector-borne infectious disease mapping with stochastic difference equations: an analysis of dengue disease in Malaysia, Journal of Applied Statistics, vol. 39(9), pp. 2029-2046. DOI: 10.1080/02664763.2012.700450, 2012.
 J. C. Robinson, An introduction to ordinary differential equations. UK: Cambridge University Press, 2004.
 I. Kalashnikova, A vector-host model for epidemics. Retrieved from http://www.stanford.edu/~irinak/Math420FinalPaper.pdf, 2004.
 D. Spiegelhalter, A. Thomas, N. Best, and D. Lunn, WinBUGS user manual version 1.4. Cambridge UK: MRC Biostatistics Unit, 2003.
 A.B. Lawson, W.J. Browne, and C.L.Vidal Rodeiro, Disease mapping with WinBUGS and MLwiN. England: John Wiley & Sons, 2003.
 H. Jusoh, J.A. Malek and A. A. Rashid, The role of efficient urban governance in managing Kuala Lumpur city-region development, Asian Social Science, Vol. 5(8), pp. 14-32,2009.
 A. Rohani, I. Asmaliza, S. Zainah, and H. L. Lee, Detection of dengue from field Aedes Aegypti and Aedes albopictus adults and larvae, Southeast Asian Journal of Tropical Medicine for Public Health, vol. 28(1), pp. 138-142, 1997.
 H.L. Lee and K. Inder Singh, Sequential sampling for Aedes Aegypti and Aedes albopictus (Skuse) adults: its use in estimation of vector density threshold in dengue transmission and control, Journal of Bioscience, vol. 2 (1 & 2), pp. 9-14, 1991.
 N.A. Samat and D.F. Percy, Predictions of Relative Risks for Dengue Disease Mapping in Malaysia based on Stochastic SIR-SI Vector-borne Infectious Disease Transmission Model, World Applied Science Journal, (in press), 2013.