Mathematical models for vector-borne infectious disease mapping with application to Dengue disease in Malaysia

Few publications consider the estimation of relative risk for vector borne infectious diseases.Most of these articles involve exploratory analysis that includes the study of covariates andtheir effects on disease distribution and the study of geographic information systems tointegrate patient-related information. The aim of this research is to introduce an alternativemethod of relative risk estimation based on stochastic SIR-SI models (susceptible-infectiverecoveredfor human populations; susceptible-infective for vector populations) for thetransmission of vector borne infectious diseases, particularly dengue disease.Firstly, we describe deterministic compartmental SIR-SI models that are suitable for denguedisease transmission. We then adapt these to develop corresponding stochastic SIR-SImodels using 'discrete time, discrete space' and 'continuous time, discrete space' data. Ourfirst type of stochastic models comprises extensions of the discrete time stochastic SIRmodel proposed by Lawson (2006) and involves the theoretical construction and iterativeevaluation of SIR-SI difference equations. Our second type of stochastic models involvescontinuous extensions of the first type of models and involves the theoretical constructionand numerical analysis of SIR-SI differential equations. Determining solutions for the lattermodels involves investigating their asymptotic properties and applying simple computationalalgorithms for solving the SIR-SI system of ordinary differential equations. Furtherdiscussion on modelling continuous space data regardless of the measurement scale of timesis also presented in this thesis.Finally, an alternative method of estimating the relative risk for dengue disease mappingbased on these stochastic SIR-SI models is developed and applied to analyse dengue datafrom Malaysia. This new approach offers better models for estimating relative risks fordengue disease mapping compared to the other common approaches, because it takes intoaccount the transmission process of the disease while allowing for covariates and spatialcorrelation between risks in adjacent regions. Although the SIR-SI model for dengue diseaseis the focus of this research, the methods extend readily to apply more generally to othervector borne infectious diseases.

Level dc:type.qualificationlevel

Doctoral (Level 8)

Year dc:date.issued

2012

Author dc:creator

• Samat, NA

Language dc:language

en

Identifier

oai:salford-repository.worktribe.com:1337835

OAI identifier oai:identifier

oai:salford-repository.worktribe.com:1337835