Trading-off lives and livelihood: optimal lockdown policy in a unified epidemic and economic framework

We propose an optimal control framework to calculate the lockdown strategy in a unified epidemic and economic model. The reward function trades off both deaths and infections in the population, as well as the impact on the economy due to the lockdown strategy. The proposed unified epidemic-economic framework uses a three-layered social interaction network, with children, adults, and elderlies forming the three layers. This allows us to impose an age group-specific lockdown while also accounting for the inter and intra-age group interactions, differences in epidemic vulnerability, and economic productivity of the three age groups. We calibrate our model for the observed real-world economic and epidemic parameters, and interaction patterns for India (a lower-middle income country) and the US (a high-income country) during the first wave of the Covid-19 pandemic. The results show that the optimal age-specific lockdown strategies are country-specific. We compare the optimal policy with easily implementable heuristic strategies for various model parameters to identify heuristics that perform closest to the optimal strategy, this is also country-specific. We find that poorly implemented heuristics (e.g., partial lockdown) sometimes perform worse than extreme strategies—full or no lockdown. We also present results for sensitivity analysis of the model parameters as their estimation may be inaccurate. Our work may be useful to policymakers, who want to trade off epidemic and economic costs, to manage a novel epidemic using partial/full lockdown for which other mitigation strategies (e.g., vaccination) are not available yet.