We study the extinction of long-lived epidemics on finite complex networksinduced by intrinsic noise. Applying analytical techniques to the stochasticSusceptible-Infected-Susceptible model, we predict the distribution of largefluctuations, the most probable, or optimal path through a network that leadsto a disease-free state from an endemic state, and the average extinction timein general configurations. Our predictions agree with Monte-Carlo simulationson several networks, including synthetic weighted and degree-distributednetworks with degree correlations, and an empirical high school contactnetwork. In addition, our approach quantifies characteristic scaling patternsfor the optimal path and distribution of large fluctuations, both near and awayfrom the epidemic threshold, in networks with heterogeneous eigenvectorcentrality and degree distributions.
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