In response to the rapid spread of the Coronavirus (COVID-19) , with ten thousands of deaths and intensive-care hospitalizations, a large number of regions and countries have been put under lockdown by their respective governments. Policy makers are confronted in this situation with the problem of balancing public health considerations , with the economic costs of a persistent lockdown. We introduce a modified epidemic model, the controlled-SIR model, in which the disease reproduction rates evolve dynamically in response to political and societal reactions. Social distancing measures are triggered by the number of infections, providing a dynamic feedback-loop which slows the spread of the virus. We estimate the total cost of several distinct containment policies incurring over the entire path of the endemic . Costs comprise direct medical cost for intensive care , the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, the total costs are highest at a medium level of reactivity when value of life costs are omitted. Very strict measures fare best, with a hands-off policy coming second. Our key findings are independent of the specific parameter estimates, which are to be adjusted with the COVID-19 research status. In addition to numerical simulations, an explicit analytical solution for the controlled continuous-time SIR model is presented. For an uncontrolled outbreak and a reproduction factor of three, an additional 28\% of the population is infected beyond the herd immunity point, reached at an infection level of 66\%, which adds up to a total of 94\% .
The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies and the need to balance public health considerations with the economic costs of a persistent lockdown. We introduce a modified epidemic model, the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment policies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated over the entire course of the epidemic . Costs comprise medical care cost , the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, strict measures fare better than a hands-off policy . Strategies based on actual case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic .
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, with ten thousands of deaths and intensive-care hospitalizations, a large number of regions and countries have been put under lockdown by their respective governments. Policy makers are confronted in this situation
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Social distancing measures are triggered by the number of infections, providing a dynamic feedback-loop which slows the spread of the virus. We estimate the total cost of several distinct containment policies incurring
An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment policies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated
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the total costs are highest at a medium level of reactivity when value of life costs are omitted. Very
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coming second. Our key findings are independent of the specific parameter estimates, which are to be adjusted with the COVID-19 research status. In addition to numerical simulations, an explicit analytical solution for the controlled continuous-time SIR model is presented. For an uncontrolled outbreak and a reproduction factor of three, an additional 28\% of the population is infected beyond the herd immunity point, reached at an infection level of 66\%, which adds up to a total of 94\%
. Strategies based on actual case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic