Managing an Epidemic Using Compartmental Models and Measure Differential Equations

Classical epidemiological models can be complemented with probabilistic ones to describe the dynamic of virus mutations. Here controlled ordinary differential equations are coupled with evolution equations for measures, called measure differential equations, to capture both the population dynamics and the virus ones. Optimal controls are then used to design non-pharmaceutical interventions minimizing the health and economic cost of a pandemic. Simulations show the capability of the model to capture observed waves and the effectiveness of optimization strategies.