Branch-and-Price for Prescriptive Contagion Analytics

TL;DR

This paper introduces a novel branch-and-price algorithm for prescriptive contagion analytics, enabling optimal resource allocation in complex, large-scale epidemic and social systems with differential constraints, significantly improving intervention effectiveness.

Contribution

It develops a new optimization framework combining set partitioning, column generation, state clustering, and a tri-partite branching scheme to solve large-scale contagion management problems.

Findings

Algorithm scales to large, complex instances

Outperforms existing benchmarks in efficiency

Can increase vaccination campaign effectiveness by 12-70%

Abstract

Predictive contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision-maker allocates shared resources across multiple segments of a population, each governed by continuous-time dynamics. We define four real-world problems under this umbrella: vaccine distribution, vaccination centers deployment, content promotion, and congestion mitigation. These problems feature a large-scale mixed-integer non-convex optimization structure with constraints governed by ordinary differential equations, combining the challenges of discrete optimization, non-linear optimization, and continuous-time system dynamics. This paper develops a branch-and-price methodology for prescriptive contagion analytics based on: (i) a set partitioning reformulation; (ii) a column generation decomposition; (iii) a state-clustering algorithm for discrete-decision continuous-state dynamic programming; and (iv) a tri-partite branching scheme to circumvent non-linearities. Extensive experiments show that the algorithm scales to very large and otherwise-intractable instances, outperforming state-of-the-art benchmarks. Our methodology provides practical benefits in contagion systems; in particular, it can increase the effectiveness of a vaccination campaign by an estimated 12-70%, resulting in 7,000 to 12,000 extra saved lives over a three-month horizon mirroring the COVID-19 pandemic. We provide an open-source implementation of the methodology in an online repository to enable replication.