Mathematical modes 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 and their  effects on disease distribution and the study of geographic information systems to integrate  patient-related information. The aim of this research is to introduce an alternative method of  relative risk estimation based on stochastic SIR-SI models (susceptible-infective-recovered for  human populations; susceptible-infective for vector populations) for the transmission of vector  borne infectious diseases, particularly dengue disease. Firstly, we describe deterministic compartmental SIR-SI models that are suitable for dengue disease  transmission. We then adapt these to develop corresponding stochastic SIR-SI models using 'discrete  time, discrete space' and 'continuous time, discrete space' data. Our first type of stochastic  models comprises extensions of the discrete time stochastic SIR model proposed by Lawson (2006) and  involves the theoretical construction and iterative evaluation of SIR-SI difference equations. Our  second type of stochastic models involves continuous extensions of the first type of models and  involves the theoretical construction and numerical analysis of SIR-SI differential equations.  Determining solutions for the latter models involves investigating their asymptotic properties and  applying simple computational algorithms for solving the SIR-SI system of ordinary differential  equations. Further discussion on modelling continuous space data regardless of the measurement  scale of times is also presented in this thesis. Finally, an alternative method of estimating the relative risk for dengue disease mapping based on  these stochastic SIR-SI models is developed and applied to analyse dengue data from Malaysia. This  new approach offers better models for estimating relative risks for dengue disease mapping compared  to the other common approaches, because it takes into account the transmission process of the  disease while allowing for covariates and spatial correlation between risks in adjacent regions.  Although the SIR-SI model for dengue disease is the focus of this research, the methods extend  readily to apply more generally to other vector borne infectious diseases.