Epidemic Extinction Paths in Complex Networks

Abstract

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large fluctuations, the most probable, or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte-Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.

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Cited by in corpus (15)

• Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations
• Markovian approach to tackle the interaction of simultaneous diseases
• Large deviations of random walks on random graphs
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Rare slips in fluctuating synchronized oscillator networks
• A general formulation of long-range degree correlations in complex networks
• Degree Dispersion Increases the Rate of Rare Events in Population Networks
• Enhancement of large fluctuations to extinction in adaptive networks
• Epidemic extinction in networks: Insights from the 12,110 smallest graphs
• Large order fluctuations, switching, and control in complex networks
• Rare events in networks with internal and external noise
• Applications of WKB and Fokker-Planck methods in analyzing population extinction driven by weak demographic fluctuations
• Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks
• Extremal statistics for first-passage trajectories of drifted Brownian motion under stochastic resetting
• Epidemic extinction in a simplicial susceptible-infected-susceptible model