Interplay of Health Interventions in Time-Varying contact Networks

Throughout history, humanity has recurrently faced epidemics of infectious diseases, which have spread both within and between populations. From ancient pandemics like the Antonine Plague to the contemporary COVID-19 pandemic, understanding and controlling the spread of diseases has always been crucial. Mathematical modeling of epidemics plays a key role in this understanding. Over the years, epidemic modeling has evolved, incorporating interdisciplinary elements, particularly from network science. Health interventions, including non-pharmaceutical measures and pharmaceutical solutions like vaccines, have historically been crucial in mitigating disease spread. During the COVID-19 pandemic, for example, measures such as social distancing, lockdowns, mask usage, hygiene, and vaccinations were key in controlling the virus spread. This thesis proposes a mathematical framework to model three distinct health interventions—social distancing, mask usage, and vaccination—on activity-driven networks (ADN), a mathematical framework that models the dynamic nature of individual contacts and the heterogeneity in sociability. We studied analytically how these interventions affect epidemic thresholds using the SIR model as an example, and validated them through numerical simulations. Two mechanisms for intervention adoption were considered: random and activity-based, focusing on nodes with the most or least number of contacts. Our findings highlight that protecting the most active nodes significantly enhances mitigation strategies. Among the three interventions, vaccines showed the best results, especially when targeted at these individuals. However, vaccines are not always available at the outbreak, therefore the use of alternative interventions remain crucial. Additionally, we examine the combination of interventions. In the first case study, we simulate scenarios where essential workers cannot reduce contacts, emphasising the importance of vaccinating and protecting these individuals. In the second case, we explore how the overlap in groups adopting interventions affects their effectiveness, showing that distributed adoption across the population leads to better results. Overall, this thesis combines mathematical evaluation and the interplay of health interventions in an activity-driven, time-varying network, enhancing the effectiveness of epidemic control strategies.