Conrad Ratchford

Multi-scale and multi-group modeling techniques applied to Cholera and COVID-19

A Dissertation Presented for the Doctor of Philosophy in Computational Science, The University of Tennessee at Chattanooga

Conrad Ratchford, August 2021

Abstract:

Cholera is an acute intestinal illness caused by infection with the Vibrio cholerae bacteria. The dynamics of the disease transmission are governed by human-human, environment-human, and within-human sub-dynamics. Specifically, the within-host dynamics incorporate virus and immune cell interaction with the vibrios. One model is presented to incorporate all three of these dynamical components. This model is extended to consider the case of a sub-divided population interacting in a spatially heterogeneous environment. In particular, we find that the between-host reproduction number is shaped by the collection of the disease risk factors from all the individual host groups. These multi-patch techniques are used to present a model of the United States outbreak of COVID-19 during the summer of 2020. The existence and uniqueness of a DFE (Disease Free Equilibrium) are discussed in light of the number R0, when applicable, as well as the existence and uniqueness of a positive EE (Endemic Equilibrium). The conditions needed to achieve local and global stability in each system are reviewed, and numerical simulations are presented to supplement these mathematical results.

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