Network-based modeling of infectious disease spillover

Abstract

This thesis contains two main chapters: Computational Epidemiology (second chapter) and SIR Epidemics in Interconnected Networks: threshold curve and phase transition (third chapter). In the second chapter, we delve into the basics and history of epidemiology to underscore the importance of understanding zoonotic diseases and the capabilities and limitations of various mathematical modeling approaches. We also discuss various mathematical modeling techniques, such as Agent-Based Modeling, Network-Based Modeling, Patch Modeling, and others. In the first part of the third chapter, we examine the Susceptible-Infected-Recovered (SIR) dynamics within interconnected networks, emphasizing the structural heterogeneity and interdependencies present in real-world systems. We demonstrate how the epidemic threshold of a contact network is affected when coupled with another network for a fixed infection strength. Our model considers both contact networks and interconnections as generic, depicting the epidemic threshold curve for interconnected networks. We assume that the infection could initially be present in either one or both networks. If the normalized infection strengths exceed the threshold curve, the infection spreads; otherwise, it does not, regardless of the interconnection level. In the second part of the third chapter, we investigate the spillover phenomenon, where a disease spreads from a reservoir network to a novel host population network. We observe a phase transition when the number of links or the inter-network infection rate surpasses a specific threshold, keeping other parameters constant. The spillover dynamics reveal two regimes: a major spillover region and a minor spillover region, determined by the fraction of interpopulation links and inter-network infection strength. High spillover probability occurs in the major spillover region, while low probability occurs in the minor region. Additionally, we find that the threshold number of links required to achieve spillover varies with network topology when the number of infected individuals within the reservoir network is nearly equal and the inter-network infection strength is constant. Overall, this work enhances the understanding of SIR dynamics in interconnected networks and provides insights into the behavior of epidemics in complex systems. It integrates a comprehensive review of computational epidemiology along with significant findings regarding the spread of disease and spillover in interconnected networks.