A control theory approach to optimal pandemic mitigation

In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while minimizing costs incurred by introduction societal measures (such as closing schools, social distancing, lockdowns, etc.), under constraint that infected fraction population does never exceed certain maximum corresponding public health system capacity. Optimality is derived and verified variational numerical methods number model cost functions. The effects immune response decay after recovery are taken into account discussed in terms feasibility strategies based on immunity.