Optimizing Social Distancing Policies: A Dynamic Programming Approach for Coupled High and Low Risk Populations

Background: Decision makers may use social distancing to reduce transmission between risk groups in a pandemic scenario like Covid-19. However, it may result in both financial, mental, and social costs. Given these tradeoffs, it is unclear when and who needs to social distance over the course of a pandemic when policies are allowed to change dynamically over time and vary across different risk groups (e.g., older versus younger individuals face different Covid-19 risks). In this study, we examine the optimal time to implement social distancing to optimize social utility, using Covid-19 as an example. Methodology: We propose using a Markov decision process (MDP) model that incorporates transmission dynamics of an age-stratified SEIR compartmental model to identify the optimal social distancing policy for each risk group over time. We parameterize the model using population-based tracking data on Covid-19 within the US. We compare results of two cases: allowing the social distancing policy to vary only over time, or over both time and population (by risk group). To examine the robustness of our results, we perform sensitivity analysis on patient costs, transmission rates, clearance rates, mortality rates. Results: Our model framework can be used to effectively evaluate dynamic policies while disease transmission and progression occurs. When the policy cannot vary by subpopulation, the optimal policy is to implement social distancing for a limited duration at the beginning of the epidemic; when the policy can vary by subpopulation, our results suggest that some subgroups (older adults) may never need to socially distance. This result may occur because older adults occupy a relatively small proportion of the total population and have less contact with others even without social distancing. Conclusion: Our results show that the additional flexibility of allowing social distancing policies to vary over time and across the population can generate substantial utility gain even when only two patient risk groups are considered. MDP frameworks may help generate helpful insights for policymakers. Our results suggest that social distancing for high-contact but low-risk individuals (e.g., such as younger adults) may be more beneficial in some settings than doing so for low-contact but high-risk individuals (e.g., older adults).