[Paper Review] A decision support system for optimizing the cost of social distancing in order to stop the spread of COVID-19

Alexandru Popa|arXiv (Cornell University)|Apr 6, 2020

COVID-19 epidemiological studies2 references5 citations

TL;DR

This paper proposes a decision support system that uses combinatorial optimization to identify cost-effective social distancing measures—such as closing specific facilities or isolating populations—to minimize disease transmission while reducing economic impact. The method formulates the problem as an NP-hard optimization task, develops a heuristic algorithm, and demonstrates via simulation that a 1% budget allocation can reduce infection risk by over 80% compared to no intervention.

ABSTRACT

Currently there are many attempts around the world to use computers, smartphones, tablets and other electronic devices in order to stop the spread of COVID-19. Most of these attempts focus on collecting information about infected people, in order to help healthy people avoid contact with them. However, social distancing decisions are still taken by the governments empirically. That is, the authorities do not have an automated tool to recommend which decisions to make in order to maximize social distancing and to minimize the impact for the economy. In this paper we address the aforementioned problem and we design an algorithm that provides social distancing methods (i.e., what schools, shops, factories, etc. to close) that are efficient (i.e., that help reduce the spread of the virus) and have low impact on the economy. On short: a) we propose several models (i.e., combinatorial optimization problems); b) we show some theoretical results regarding the computational complexity of the formulated problems; c) we give an algorithm for the most complex of the previously formulated problems; d) we implement and test our algorithm; and e) we show an integer linear program formulation for our problem.

Motivation & Objective

• To address the lack of automated tools for governments to make optimal social distancing decisions.
• To minimize disease transmission while reducing economic disruption from lockdowns.
• To design a computationally efficient algorithm for large-scale social distancing planning.
• To provide a decision framework that balances public health and economic costs.

Proposed method

• The problem is modeled as a combinatorial optimization task on a complete graph where nodes represent individuals and edges represent contact probabilities.
• Each individual has associated risk and vulnerability values, and each facility has a cost and reduction factor for contact probability.
• The core problem is formulated as an NP-hard optimization task to minimize overall population risk under a budget constraint.
• A heuristic polynomial-time algorithm is proposed to solve the NP-hard problem efficiently.
• An integer linear programming (ILP) formulation is provided for completeness, though it is only feasible for small datasets.
• Simulations use synthetic data with power-law distributions to model real-world social networks and facility costs.

Experimental results

Research questions

• RQ1 What social distancing measures (e.g., closing schools, factories) minimize disease spread under a fixed budget?
• RQ2 How can the trade-off between public health impact and economic cost be optimized in real-time decision-making?
• RQ3 Can a small budget (e.g., 1% of total cost) significantly reduce infection risk compared to no intervention?
• RQ4 How does the algorithm perform under varying network structures and cost distributions?
• RQ5 What is the computational feasibility of solving this problem exactly, and how effective is the heuristic?

Key findings

• With only 1% of the total cost required to close all facilities, the algorithm reduces population infection risk by more than 80% compared to no intervention.
• Even with a 10% budget, the system reduces risk to less than 20% of the original level, demonstrating high efficiency.
• The algorithm performs well under diverse cost distributions, including normal distributions with μ=1.1 and σ=0.4 or 0.5.
• The power-law exponent α₂ had minimal impact on overall risk when infection proportions followed a power-law distribution.
• The heuristic algorithm scales effectively, enabling practical deployment on large synthetic networks.
• The ILP formulation is provided for completeness, though it is computationally infeasible for large-scale real-world applications.