Changing environmental conditions can significantly affect the dynamics of disease spread. These changes may arise naturally or result from human interventions; in the latter case, lockdown measures that lead to abrupt but temporary reductions in transmission rates are used to combat disease spread. Yet, the impact of these measures on rare events in heterogeneous populations remains understudied. Here, we analyze the susceptible-infected-susceptible (SIS) model in a stochastic setting where disease extinction—a sudden clearance of the infection—–occurs via a rare, large fluctuation. We use a semiclassical approximation and numerical simulations on heterogeneous assortative networks, with degree-degree correlations between neighboring nodes, to show how the extinction risk of the disease depends on the lockdown's duration and magnitude, and on the network topology.

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• Complex networks
• Homogeneous networks
• Epidemic spreading
• Large deviation & rare event statistics
• Monte Carlo methods
• SIS model
• Semiclassical methods