Learning Fair Policies for Infectious Diseases Mitigation using Path Integral Control

TL;DR

The paper tackles the problem of designing fair, region-specific disease mitigation policies under uncertainty by coupling a stochastic multi-group SIR model with an unfairness penalty. It introduces path integral control as an efficient, optimization-free method to solve the resulting nonlinear stochastic control problem, using a logarithmic transformation and the Feynman-Kac representation. A COVID-19 case study demonstrates that fairness-aware policies can reduce inter-regional disparities—achieved, for example, by prioritizing vaccination in lower-income regions—with only modest increases in overall costs. The work provides actionable insights for policymakers on balancing equity and efficiency in epidemic response through region-aware interventions and a tunable fairness parameter $\eta$. The approach has potential implications for structuring equitable public health strategies in future outbreaks using scalable Monte Carlo-based control.

Abstract

Infectious diseases pose major public health challenges to society, highlighting the importance of designing effective policies to reduce economic loss and mortality. In this paper, we propose a framework for sequential decision-making under uncertainty to design fairness-aware disease mitigation policies that incorporate various measures of unfairness. Specifically, our approach learns equitable vaccination and lockdown strategies based on a stochastic multi-group SIR model. To address the challenges of solving the resulting sequential decision-making problem, we adopt the path integral control algorithm as an efficient solution scheme. Through a case study, we demonstrate that our approach effectively improves fairness compared to conventional methods and provides valuable insights for policymakers.

Figures (4)

• Figure 1: Mean evolution (solid lines) of the infected $I_j(t)$ (first row) and deceased $D_j(t)$ (second row) over 500 simulations across different regions---upper (green), middle (red), and lower (blue) income groups with shaded areas representing the 10th and 90th percentiles: the first column presents test performance under the homogeneous policy based on the single-group SIR model, while the remaining columns show results for our region-specific policy derived from the multi-group SIR model with varying penalty parameter $\eta$. Increasing $\eta$ significantly mitigates the effects of the disease in the lower-income region.
• Figure 2: Mean control inputs for vaccination $V_j(t)$ (first row) and lockdown $L_j(t)$ (second row) policies over 500 simulations: the first column shows the mean control input (purple) under the homogeneous policy based on the single-group SIR model. The remaining columns represent our region-specific policy for the multi-group SIR model with varying penalty parameters $\eta$ across different regions—upper (green), middle (red), and lower (blue) income groups. Increasing $\eta$ results in significantly different vaccination policies, particularly in the lower-income region.
• Figure 3: Cost-unfairness Pareto frontier: mean values of economic loss plus control cost and unfairness measure for our multi-region SIR model (blue) over 500 simulations are shown. For example, comparing with the homogeneous policy (purple), the policy that ignores the unfairness measure ($\eta=0$) achieves better performance in both fairness and costs, i.e., a lower unfairness measure and costs. There is a clear trade-off between costs and fairness. The relatively flat curve up to $\eta=0.05$ suggests that fairness can be significantly improved with small additional costs.
• Figure 4: Mean runtime (blue) for computing \ref{['eq:approx_control_main']} at the initial time step ($k=0$) with $K=180$ (as in our case study) and mean test performance (red) over 30 simulations with varying numbers of sample trajectories $M$.

Theorems & Definitions (3)

• Definition 1: Economic Disparity Unfairness Measure
• Remark 1: Measures of Health Inequalities
• Remark 2