Controlling Epidemic Spread Under Immunization Delay Constraints

TL;DR

This paper addresses the challenge of controlling epidemic spread by developing a greedy vaccination strategy that accounts for immunization delays, maximizing the expected number of saved nodes in complex infection scenarios.

Contribution

It formulates the vaccination problem with delay constraints as a monotone submodular maximization and proposes a greedy algorithm with proven approximation guarantees.

Findings

Greedy algorithm achieves a (1 - 1/e) approximation ratio.

Algorithm outperforms baseline strategies in simulations.

Extends to multiple infection sources with systematic application.

Abstract

In this paper, we study the problem of minimizing the spread of a viral epidemic when immunization takes a non-negligible amount of time to take into effect. Specifically, our problem is to determine which set of nodes to be vaccinated when vaccines take a random amount of time in order to maximize the total reward, which is the expected number of saved nodes. We first provide a mathematical analysis for the reward function of vaccinating an arbitrary number of nodes when there is a single source of infection. While it is infeasible to obtain the optimal solution analytically due to the combinatorial nature of the problem, we establish that the problem is a monotone submodular maximization problem and develop a greedy algorithm that achieves a $(1\!-\!1/e)$-approximation. We further extend the scenario to the ones with multiple infection sources and discuss how the greedy algorithm can be applied systematically for the multiple-source scenarios. We finally present extensive simulation results to demonstrate the superiority of our greedy algorithm over other baseline vaccination strategies.