abstract: In this dissertation the potential impact of some social, cultural and economic factors on Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is addressed. A mathematical model, calibrated with data from the 2014 West African outbreak, is used to show the dynamics of EVD control under various quarantine and isolation effectiveness regimes. It is shown that in order to make a difference it must reach a high proportion of the infected population. The effect of EVD-dead bodies has been incorporated in the quarantine effectiveness. In Chapter four, the potential impact of differential risk is assessed. A two-patch model without explicitly incorporate quarantine is used to assess the impact of mobility on communities at risk of EVD. It is shown that the overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed. The cost that individuals in the low-risk patch must pay, as measured by secondary cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine levels is used to show that quarantine a large enough proportion of the population under effective isolation leads to a measurable reduction of secondary cases in the presence of mobility. It is shown that sharing limited resources can improve the effectiveness of EVD effective control in the two-patch high-low risk system. Identifying the conditions under which the low-risk community would be willing to accept the increases in EVD risk, needed to reduce the total number of secondary cases in a community composed of two patches with highly differentiated risks has not been addressed. In summary, this dissertation looks at EVD dynamics within an idealized highly polarized world where resources are primarily in the hands of a low-risk community – a community of lower density, higher levels of education and reasonable health services – that shares a “border” with a high-risk community that lacks minimal resources to survive an EVD outbreak. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2018

Heterogeneity, influenced by diverse factors such as age, gender, immunity, behavior, and spatial distribution, plays a critical role in the dynamics of infectious disease transmission. Discrete mathematical structures, including matrices and graphs, can offer effective tools for modeling the interactions among these diverse factors, resulting heterogeneous epidemiological models. This dissertation explores analytical approaches, specifically utilizing eigenvalues and eigenvectors of discrete structures, to characterize heterogeneity within mathematical models of infectious diseases. Theoretical results, along with numerical simulations, enhance our understanding of heterogeneous epidemiological processes and their significant implications for disease control strategies. In this dissertation, we introduce a unified approach to establish the final size formula in heterogeneous epidemic models, based on a new concept of “total infectious contacts” as an eigenvector-based aggregation of disease compartments. This approach allows us to identify the peak of total infectious contacts, offering a novel method to pinpoint the turning point of a disease outbreak. Furthermore, we examine spatial heterogeneity through two distinct mathematical frameworks: the Lagrangian and Eulerian models. The Lagrangian model assesses the epidemiological consequences of spatio-temporal residence time matrices, while the Eulerian model investigates “Turing instability” as a new underlying mechanism for spatial heterogeneity observed in disease prevalence data.