Mathematics of Viral Infections: A Review of Modeling Approaches and A Case-Study for Dengue Dynamics

Abstract

In this thesis we use mathematical models to study the mechanisms by which diseases spread. Transmission dynamics is modelled by the class of SIR models, where the abbreviation stands for susceptible (S), infected (I) and recovered (R). These models are also called compartmental models, and they serve as the basic mathematical framework for understanding the complex dynamics of infectious diseases. Theory developed for the SIR framework can be applied the real-world dynamics, for instance to the spread of the dengue virus. We look at how parameters such as the as basic reproduction number, R0, drive epidemics by allowing transitions from a disease-free equilibrium (DFE) when R0 < 1 to an endemic equilibrium (EE) when R0 > 1. A case study was carried out to investigate dengue transmission dynamics in a single serotype model by using a vector-to-human compartmental model. Here the approach is to explore the underlying dynamical structures, as well as looking at the projected impact of possible interventions such as vaccines and vector-control measures.