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-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.
Abstract: Dengue disease is an infectious vector-borne viral
disease that is commonly found in tropical and sub-tropical regions,
especially in urban and semi-urban areas, around the world and
including Malaysia. There is no currently available vaccine or
chemotherapy for the prevention or treatment of dengue disease.
Therefore prevention and treatment of the disease depend on vector
surveillance and control measures. Disease risk mapping has been
recognized as an important tool in the prevention and control
strategies for diseases. The choice of statistical model used for
relative risk estimation is important as a good model will
subsequently produce a good disease risk map. Therefore, the aim of
this study is to estimate the relative risk for dengue disease based
initially on the most common statistic used in disease mapping called
Standardized Morbidity Ratio (SMR) and one of the earliest
applications of Bayesian methodology called Poisson-gamma model.
This paper begins by providing a review of the SMR method, which
we then apply to dengue data of Perak, Malaysia. We then fit an
extension of the SMR method, which is the Poisson-gamma model.
Both results are displayed and compared using graph, tables and
maps. Results of the analysis shows that the latter method gives a
better relative risk estimates compared with using the SMR. The
Poisson-gamma model has been demonstrated can overcome the
problem of SMR when there is no observed dengue cases in certain
regions. However, covariate adjustment in this model is difficult and
there is no possibility for allowing spatial correlation between risks in
adjacent areas. The drawbacks of this model have motivated many
researchers to propose other alternative methods for estimating the
risk.