MATHEMATICAL EPIDEMIOLOGY: MODELING OF INFECTIOUS DISEASE

Abstract

The ongoing coronavirus pandemic, caused by severe acute respiratory syndrome coronavirus2 was first identified in December 2019. This dissertation falls into the field of mathematical modelling of infectious diseases. It is composed of two parts: modeling the spread of Covid19, with an application to the Hawaiian archipelago; development of classification tools for the comparison of the evolution of the Covid-19 pandemic at different geographic locations. First we present a generalized discrete deterministic compartmental SEIR model for the spread of Covid-19 which incorporates competing variants of the virus, vaccination, fading of vaccine protection, the possibility of a previously infected individual becoming susceptible and travel restrictions. Using this model on the counties of the State of Hawai‘i , we study the impacts of mitigation measures and the impacts of tourism on the spread of the disease among the local population. Second, we focus on some classification tools. The notion of wave is used to describe the evolution of a pandemic but although the terminology is often used, the current literature does not have a precise definition for it. In this dissertation, we provide a mathematical definition for the notion of a wave and present an algorithm to detect waves from a given set of data. In addition, comparison of the evolution in time of different spread of a disease is also not well addressed in the literature. Here, we introduce topological structures associated to data representing the spread of daily cases or hospital data and define an orientation preserving pseudo-metric on them that can be used to compare the evolution of pandemic between different regions.