[Paper Review] A Multi-Stage Stochastic Programming Approach to Epidemic Resource Allocation with Equity Considerations

Xuecheng Yin, İ. Esra Büyüktahtakın|arXiv (Cornell University)|Feb 23, 2021

Viral Infections and Outbreaks Research70 references4 citations

TL;DR

This paper proposes a multi-stage stochastic programming model that optimizes epidemic resource allocation under uncertainty, integrating disease progression and equity considerations. It minimizes total infections and fatalities while ensuring fairness through novel infection and capacity equity metrics, demonstrating that proportional allocation based on population is suboptimal and costly in terms of health outcomes.

ABSTRACT

Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals. We define two new equity metrics, namely infection and capacity equity, and explicitly consider equity for allocating treatment funds and facilities over multiple time stages. We also study the multi-stage value of the stochastic solution (VSS), which demonstrates the superiority of the proposed stochastic programming model over its deterministic counterpart. We apply the proposed formulation to control the Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and fair resource-allocation strategies. Our model balances the proportion of infections over all regions, even without including the infection equity or prevalence equity constraints. Model results also show that allocating treatment resources proportional to population is sub-optimal, and enforcing such a resource allocation policy might adversely impact the total number of infections and deaths, and thus resulting in a high cost that we have to pay for the fairness. Our multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

Motivation & Objective

• To address the limitation of existing compartmental models in optimizing resource allocation under disease growth uncertainty.
• To develop a stochastic programming framework that integrates uncertain disease progression with dynamic resource allocation over multiple time stages.
• To explicitly incorporate equity—defined as infection and capacity equity—into the optimization of treatment center and resource distribution.
• To evaluate the value of the stochastic solution (VSS) and demonstrate the superiority of the stochastic model over deterministic counterparts.
• To provide a practical, adaptable model for controlling infectious diseases in meta-populations and dynamically evolving outbreaks.

Proposed method

• Formulates a multi-stage stochastic mixed-integer programming model to optimize treatment center placement and resource distribution across regions over time.
• Incorporates scenario-based uncertainty in disease transmission rates, using bi-weekly transmission parameters for Guinea, Sierra Leone, and Liberia.
• Introduces two new equity metrics: infection equity (balancing regional infection proportions) and capacity equity (balancing access to treatment capacity).
• Uses a chance-constrained approach to enforce equity constraints with a tolerance parameter k, allowing for flexible fairness trade-offs.
• Employs a decomposition-based solution algorithm to handle the computational complexity of the large-scale stochastic model.
• Validates the model using real-world Ebola outbreak data from West Africa (2014–2016), including transmission rates, fatality rates, and burial practices.

Experimental results

Research questions

• RQ1 How does incorporating stochasticity in disease progression improve the performance of epidemic resource allocation models compared to deterministic approaches?
• RQ2 To what extent can equity in infection and treatment capacity be achieved without explicitly constraining fairness, and what is the trade-off with overall epidemic control?
• RQ3 What is the impact of allocating resources proportionally to population size on total infections and fatalities, and is this policy optimal?
• RQ4 How do equity constraints affect computational complexity and solution time in a multi-stage stochastic epidemic model?
• RQ5 What is the value of the stochastic solution (VSS), and how does it demonstrate the advantage of stochastic over deterministic modeling in epidemic planning?

Key findings

• The proposed stochastic model reduces the total expected number of infections and funerals by 23% compared to a deterministic counterpart, demonstrating the value of the stochastic solution (VSS).
• Allocating treatment resources proportionally to population size leads to a 15% increase in total infections and a 20% increase in fatalities, indicating it is suboptimal and costly.
• Even without explicit equity constraints, the model naturally balances infection proportions across regions, with regional infection ratios differing from population ratios by at most 0.42, 0.04, and 0.38 in Guinea, Sierra Leone, and Liberia, respectively.
• Introducing infection equity constraints increased the average CPU time from 7,200 seconds to 10 hours (36,068 seconds) for k = 0.2, with a 29% optimality gap, highlighting the computational cost of enforcing fairness.
• The prevalence equity constraint, with k values as low as 3×10⁻⁹, resulted in minimal changes to budget allocation and only slight reductions in infections and funerals, suggesting that fairness is inherently balanced in the model’s solution.
• The model’s solution remains robust across different k values for both equity constraints, with no significant change in optimal budget allocation or total infections, indicating stability in the optimization outcome.