The Cost of Uncertainty in Curing Epidemics

TL;DR

This paper investigates how imperfect information affects the cost and time to cure epidemics on networks, revealing that even slight uncertainties can significantly increase resource requirements and cure times.

Contribution

It establishes fundamental bounds on curing costs under uncertainty, showing that partial information drastically changes the efficiency compared to perfect knowledge.

Findings

Minor diagnostic inaccuracies lead to exponential increases in curing time.

Perfect information allows for sublinear curing times, unlike uncertain scenarios.

Uncertainty fundamentally alters the resource-efficiency tradeoff in epidemic control.

Abstract

Motivated by the study of controlling (curing) epidemics, we consider the spread of an SI process on a known graph, where we have a limited budget to use to transition infected nodes back to the susceptible state (i.e., to cure nodes). Recent work has demonstrated that under perfect and instantaneous information (which nodes are/are not infected), the budget required for curing a graph precisely depends on a combinatorial property called the CutWidth. We show that this assumption is in fact necessary: even a minor degradation of perfect information, e.g., a diagnostic test that is 99% accurate, drastically alters the landscape. Infections that could previously be cured in sublinear time now may require exponential time, or orderwise larger budget to cure. The crux of the issue comes down to a tension not present in the full information case: if a node is suspected (but not certain) to be infected, do we risk wasting our budget to try to cure an uninfected node, or increase our certainty by longer observation, at the risk that the infection spreads further? Our results present fundamental, algorithm-independent bounds that tradeoff budget required vs. uncertainty.