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?:abstract
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An extended SIR model, including several features of the recent COVID-19 outbreak, is considered: the infected and recovered individuals can either be detected or undetected and we also integrate an intensive care unit (ICU) capacity We identify the optimal policy for controlling the epidemic dynamics using both lockdown and detection intervention levers, and taking into account the trade-off between the sanitary and the socio-economic cost of the pandemic, together with the limited capacity level of ICU With parametric specification based on the COVID-19 literature, we investigate the sensitivities of various quantities on the optimal strategies The optimal lockdown policy is structured into 4 phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion;second a short transition to reduce the prevalence of the virus;third a long period with full ICU capacity and stable virus prevalence;finally a return to normal social interactions with disappearance of the virus The optimal scenario avoids the second wave of infection, provided the lockdown is released sufficiently slowly Whenever massive resources are introduced to detect infected individuals, the pressure on social distancing can be released, whereas the impact of detection of immune individuals reveals to be more moderate
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