# A Multi-Stage Stochastic Programming Approach to Epidemic Resource Allocation with Equity Considerations

**Authors:** Xuecheng Yin, I. Esra Buyuktahtakin  
**arXiv:** [2102.11814](https://arxiv.org/abs/2102.11814)  
**Date:** 2021-02-23  
**Summary page:** https://www.summarizepaper.com/en/paper/2102.11814v1/

## Key points

- Existing compartmental models in epidemiology have limitations in optimizing resource allocation for controlling an epidemic outbreak under disease growth uncertainty
- Researchers propose a multi-stage stochastic programming compartmental model that integrates uncertain disease progression and resource allocation to control infectious disease outbreaks
- The proposed model 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
- Two new equity metrics, infection, and capacity equity are defined to allocate treatment funds and facilities over multiple time stages
- The concept of multi-stage value of the stochastic solution (VSS) is introduced, demonstrating the superiority of their proposed stochastic programming model over its deterministic counterpart.
- The proposed formulation is applied to control Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia in West Africa.
- Results show that allocating treatment resources proportional to population is sub-optimal.
- Fairness has not been studied before within the context of resource allocation for epidemiology.
- This multi-stage stochastic epidemic-logistics model can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

## Summary

This study addresses the limitations of existing compartmental models in epidemiology which struggle to optimize resource allocation for controlling an epidemic outbreak under disease growth uncertainty. The researchers present a multi-stage stochastic programming compartmental model that integrates uncertain disease progression and resource allocation to control infectious disease outbreaks. This proposed model 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. The study defines two new equity metrics, namely infection and capacity equity, explicitly considering equity for allocating treatment funds and facilities over multiple time stages. The researchers also introduce the concept of multi-stage value of the stochastic solution (VSS), demonstrating the superiority of their proposed stochastic programming model over its deterministic counterpart. To determine optimal and fair resource-allocation strategies, the proposed formulation is applied to control Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia in West Africa. The model balances the proportion of infections across all regions even without including infection equity or prevalence equity constraints. Results show that allocating treatment resources proportional to population is sub-optimal. Enforcing such a resource allocation policy might adversely impact the total number of infections and deaths resulting in a high cost paid for fairness. The study also highlights how fairness has not been studied before within the context of resource allocation for epidemiology; a literature review by (1994) presented various mathematical methods for equity measures in facility-location decision models but did not consider fairness within epidemiological contexts. Overall, this multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations. It provides a valuable tool for policymakers to make informed decisions about resource allocation during an epidemic outbreak while ensuring fairness across different regions.