The COVID-19 pandemic has had an unprecedented impact on global health and the economy since its inception in December, 2019 in Wuhan, China. Non-pharmaceutical interventions (NPI) like lockdowns and curfews have been deployed by affected countries for controlling the spread of infections. In this paper, we develop a Mixed Integer Non-Linear Programming (MINLP) epidemic model for computing the optimal sequence of NPIs over a planning horizon, considering shortages in doctors and hospital beds, under three different lockdown scenarios. We analyse two strategies - centralised (homogeneous decisions at the national level) and decentralised (decisions differentiated across regions), for two objectives separately - minimization of infections and deaths, using actual pandemic data of France. We linearize the quadratic constraints and objective functions in the MINLP model and convert it to a Mixed Integer Linear Programming (MILP) model. A major result that we prove analytically, is that the optimal sequence of NPIs always follows a decreasing severity pattern. Using this property, we further simplify the MILP model into an Integer Linear Programming (ILP) model, reducing computational time up to 99%. Our numerical results show that a decentralised strategy is more effective in controlling infections for a given severity budget, yielding up to 20% lesser infections, 15% lesser deaths and 60% lesser shortages in healthcare resources.
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