# A stochastic framework to assess the optimal allocation of limited vaccine doses in foot-and-mouth disease outbreaks using game theory

## TL;DR

This paper presents a game theory-based framework to help allocate limited vaccines during foot-and-mouth disease outbreaks, aiming to improve decision-making for policymakers.

## Contribution

The study introduces a novel stochastic framework combining game theory and allocation rules to optimize vaccine distribution during FMD outbreaks.

## Key findings

- Equal prioritization of vaccine allocation (Rule 3) most frequently resulted in Pareto optimal solutions, benefiting both the index state and neighboring states.
- Pareto optimal solutions under Rules 1–3 did not consistently lead to better outbreak control compared to Nash equilibrium solutions.
- Allocation based on dairy cattle percentage (Rule 4) showed less differentiation in outbreak outcomes between decision positions.

## Abstract

The necessary response to a livestock transboundary infectious disease outbreak will likely outpace available resources. Consequently, policymakers need strategies to inform decisions about allocating limited resources. This study aimed to develop a stochastic framework that strategically examines vaccine allocation in a series of simultaneous multi-player decision sets, using game theory and allocation rules.

We modeled 11 stochastic foot-and-mouth disease (FMD) scenarios using InterSpread Plus (Version 6.01.44). Stakeholders were designated as decision-maker one (DM1, the index state) and decision-maker two (DM2, a group of three neighboring states) requesting all or a share of the available vaccines. We selected two outcome criteria for examination: outbreak size and duration. Vaccine allocation strategies were determined by four rules. Rule 1 prioritized allocation to the index state, rule 2 prioritized allocation to neighboring states, rule 3 provided equal prioritization, and rule 4 prioritized allocation based on the percentage of dairy cattle in each state. For each scenario, 300 iterations were completed using matched random seeds. The outcome rankings of each matched iteration were treated as the payoffs of DMs and were analyzed as static games with perfect information. Nash equilibrium and Pareto optimal solutions were summarized across scenarios and iterations within each rule. Decision positions were evaluated per allocation rule according to game theory equilibrium principles.

Rule 3, equal prioritization, resulted in a Pareto optimal solution more frequently, benefiting both DMs, and had the highest level of agreement in decision-states between Nash equilibrium and Pareto optimal outcomes. For rules 1–3, Pareto optimal solutions did not consistently result in lower outbreak size and duration (90th percentile) for both DMs when compared to Nash equilibrium solutions. Under rule 4, outbreak size and duration metrics showed less differentiation between decision positions.

This stochastic framework incorporates epidemiological data and accounts for the payoffs resulting from multiple stakeholders’ choices. This approach can aid in decision-making for scarce resource allocation in contexts where individual payoffs depend on others’ choices. Additionally, these findings contribute to improving preparedness for an outbreak of FMD in disease-free regions.