A control theory approach to optimal pandemic mitigation

Abstract

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 the costs incurred by the introduction of societal control measures (such as closing schools, social distancing, lockdowns, etc.), under the constraint that the infected fraction of the population does never exceed a certain maximum corresponding to public health system capacity. Optimality is derived and verified by variational and numerical methods for a number of model cost functions. The effects of immune response decay after recovery are taken into account and discussed in terms of the feasibility of strategies based on herd immunity.

Error in Fig. 6 corrected (red curve for infinite immune response was flawed)

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• On Control of Epidemics with Application to COVID-19
• Optimization strategies of human mobility during the COVID-19 pandemic: A review
• Joint economic and epidemiological modelling of alternative pandemic response strategies