MATHEMATICAL EPIDEMIOLOGY: MODELING OF INFECTIOUS DISEASE
Date
2023
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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.
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Applied mathematics, Covid-19, Hawai'i, Interleaving Distance, Merge Trees, SEIR Model, Wave Definition
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