Epidemic extinction in networks: Insights from the 12,110 smallest graphs

Abstract

We investigate the expected time to extinction in the susceptible-infectious-susceptible (SIS) model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time exactly for all connected graphs with three to eight vertices. This approach enables us to discover descriptive relations that would be impossible with stochastic simulations. It also helps us discovering graphs and configurations of S and I with anomalous behaviors with respect to disease spreading. We find that for large transmission rates the extinction time is independent of the configurations, just dependent on the graph. In this limit, the number of vertices and edges determine the extinction time very accurately (deviations primarily coming from the fluctuations in degrees). We find that the rankings of configurations with respect to extinction times at low and high transmission rates are correlated at low prevalences and negatively correlated for high prevalences. The most important structural factor determining this ranking is the degrees of the infectious vertices.

arXiv commentv2 has some minor bug fixes

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Cited by in corpus (8)

• Influential spreaders for recurrent epidemics on networks
• Degree Dispersion Increases the Rate of Rare Events in Population Networks
• Statistical Analysis of Tipping Pathways in Agent-Based Models
• Multistage onset of epidemics in heterogeneous networks
• SIS model of disease extinction on heterogeneous directed population networks
• Influence of individual nodes for continuous-time Susceptible-Infected-Susceptible dynamics on synthetic and real-world networks
• Expected Extinction Times of Epidemics with State-Dependent Infectiousness
• How network properties and epidemic parameters influence stochastic SIR dynamics on scale-free random networks