Impact of Network Structure on Optimal Vaccination and Lockdown Policies

We formulate an optimal control problem to obtain combined vaccination and lockdown strategies under various physical constraints. A unified degree-based susceptible-infected-recovered-vaccinated-dead (SIRVD) epidemic model and an interaction-based economic model are used for this purpose. The reward function accounts for economic losses resulting from lockdowns, the cost of vaccinating the population, and losses due to deaths and infections. The optimal solution determines the duration of lockdown before resuming economic activities and identifies the priority order for vaccinating individuals. We calibrate our model with Covid-19 and economic data for India and the US, studying how optimal strategies vary with network structures in both countries. For easier implementation, we identify simple heuristic strategies specific to each country that are closest to the optimal strategies. Additionally, we conduct a sensitivity analysis to assess the robustness of our solutions and explore how the optimal strategies respond to changes in model parameters. This integrated framework can provide actionable insights to support policymakers in designing effective vaccination and lockdown strategies during public health emergencies.