We formulate an optimal-control problem for the control of the outbreak of COVID-19 in Ireland. The model equations are a standard multi-compartment SEIR model. Using standard techniques, we fit the model to the first wave of the COVID-19 outbreak in Ireland (March-May 2020). We then look at counterfactual scenarios, with a view to controlling the epidemic in the optimal way. The controls correspond to reductions in social contacts. At the same time, we impose state constraints on the model, which correspond to keeping ICU admissions below a threshold. The controls carry an economic cost: we seek to minimize this cost while satisfying the state constraints. This is a difficult problem to solve analytically, so we resort to a range of numerical optimization techniques. The computed solutions of the resulting optimization problem show that the cheapest strategy is elimination, rather than "living with the virus".
A recording of Lennon's talk can be found here.