Epidemics on Networks

TL;DR

This paper investigates how network topology influences epidemic spread by simulating $SIR$ and $SIRS$ dynamics on synthetic (ER, WS, BA) and real-world networks. It confirms the known result that scale-free networks with degree distribution $P(k)\sim k^{-\gamma}$ and $\gamma \in (2,3)$ exhibit no finite epidemic threshold, while denser or non-scale-free networks display threshold-like behavior. The work also shows that network density and the presence of hubs strongly modulate outbreak size and peak timing, and that interventions that simultaneously reduce $\beta$ and the number of contacts can appreciably curb spread. Finally, extending to $SIRS$ reveals oscillatory waves and a diminished dependence on instantaneous topology in the long term, underscoring the value of timely, contact-reduction strategies in real pandemics.

Abstract

Despite centuries of work on containment and mitigation strategies, infectious diseases are still a major problem facing humanity. This work is concerned with simulating heterogeneous contact structures and understanding how the structure of the underlying network affects the spread of the disease. For example, it has been empirically demonstrated and validated that scale free networks do not have an epidemic threshold. Understanding the relationship between network structure and disease dynamics can help to develop better mitigation strategies and more effective interventions.

Figures (7)

• Figure 2: Epidemic scope simulation on synthetic networks
• Figure 3: Epidemic scope simulation on real world networks
• Figure 4: Network comparison
• Figure 5: Comparison of Network Densities
• Figure 6: Comparison of Intervention Times