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

Samat, NA

Abstract

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-infectiverecovered
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.

Citation

Samat, N. Mathematical models for vector-borne infectious disease mapping with application to Dengue disease in Malaysia. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Aug 4, 2021
• Additional Information: Funders : Ministry of Higher Education, Malaysia;Universiti Pendidikan Sultan Idris
• Award Date: Jan 1, 2012