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An Optimal Control Approach to Covid-19

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If you have a question about this talk, please contact Thiago Burghi.

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Most countries have controlled the spread of the Covid-19 pandemic by reducing social interaction. This has drastically reduced their economic activity, and a legitimate question is “Is the cure worse than the disease?” In this presentation we show a methodology for answering this and related questions, and for assessing the appropriate policy. The problem is posed as a classical optimal control problem and solved numerically under various assumptions. We assume that no vaccine is available for one year, so that the control input is the severity of social regulation. The costs are a combination of economic damage and lives lost. Parameters are chosen to be plausible for the British case. The presentation will demonstrate how control theorists can contribute to the pandemic problem currently facing the whole world. It will introduce the standard model used in epidemiology, and discuss some variations. It will then show how the problem can be posed as an optimal control problem, and how it can be solved. A trade-off between economic damage and the number of deaths is obtained, and a surprising discontinuity is demonstrated. We consider the effects of introducing “test and trace” capability, and the effect of delay in introducing social restrictions. We also discuss how this approach should be modified for real-time policy making, and note some other work on Covid-19 by other Control researchers.

This talk is based on the recently-published paper “A cost-benefit analysis of the Covid-19 disease” by Robert Rowthorn and Jan Maciejowski, published in the Oxford Review of Economic Policy, special issue on the Covid-19 pandemic.

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This talk is part of the CUED Control Group Seminars series.

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