A modeling framework for spatial transmission of Covid-19 in local communities
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COVID-19 is the recent infectious disease caused by the severe acute respiratory syndrome novel coronavirus (SARS-CoV-2). Because the transmissibility of the virus is relatively high and the outbreaks remained undetected for several days, COVID-19 turned into a global pandemic. Almost all countries in the world have been exposed to the virus. Just in the United States, the COVID-19 cases are over 75 million, with more than 886K deaths as of February 2022. The pandemic duration and the enormous impacts on societies, economies, and public health have substantially affected the importance of conducting mathematical and statistical tools to analyze and predict the spatial transmission dynamics of COVID-19, which could provide invaluable benefits to global public health to reduce the chances of emerging new waves and control the epidemic. The current mathematical and statistical models have proved insufficient due to the lack of human behavioral and social processes, which have appeared to be vital to understanding the course of the pandemic. This dissertation proposes incorporating human behavioral, demographical, and beliefs processes to improve the accuracy of the current mathematical and statistical models. These processes include structural characteristics associated with race, ethnicity, and gender, as well as the mobility of individuals within and between local communities and beliefs about accepting or rejecting vaccinations. We focused on two modeling approaches to evaluate their capabilities and usefulness in predicting and analyzing the spatial dynamics of the disease associated with the processes mentioned earlier. The first approach is statistical modeling, implemented with SaTScan. It enabled us to identify periodic spatial-temporal COVID-19 clusters and the location of their probability of occurrence and assess the spatial clusters with respect to demographic factors of gender, race, and ethnicity. The second approach is mathematical modeling with Ordinary Differential Equations (ODE). We developed a mathematical model to describe the spatial spread of COVID-19 within and between clusters and investigated the global impacts of population movements from and to the local clusters on the spatial spread of COVID-19. Moreover, we utilized the method of Hopf bifurcation to test whether the oscillations in the COVID-19 cases are due to the natural characteristics of host-pathogen interactions.
Table of Contents
Introduction -- Spatial methods in epidemiology -- Prospective spatial-temporal clusters of COVID-19 -- Assessment of retrospective spatial clusters of COVID-19 with respect to demographic factors -- Modeling COVID-19 transmission within and between the spatial clusters -- Incorporating global dynamics to improve the accuracy of SIR Model -- Periodic waves of COVID-19 emerged from Hopf bifurcation -- Conclusions and future work -- Appendix A. Supplementary documents
Ph.D. (Doctor of Philosophy)