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We demonstrate the ability of statistical data assimilation to identify themeasurements required for accurate state and parameter estimation in anepidemiological model for the novel coronavirus disease COVID-19. Our contextis an effort to inform policy regarding social behavior, to mitigate strain onhospital capacity. The model unknowns are taken to be: the time-varyingtransmission rate, the fraction of exposed cases that require hospitalization,and the time-varying detection probabilities of new asymptomatic andsymptomatic cases. In simulations, we obtain accurate estimates of undetected(that is, unmeasured) infectious populations, by measuring the detected casestogether with the recovered and dead - and without assumed knowledge of thedetection rates. Given a noiseless measurement of the recovered population,excellent estimates of all quantities are obtained using a temporal baseline of101 days, with the exception of the time-varying transmission rate at timesprior to the implementation of social distancing. With low noise added to therecovered population, accurate state estimates require a lengthening of thetemporal baseline of measurements. Estimates of all parameters are sensitive tothe contamination, highlighting the need for accurate and uniform methods ofreporting. The aim of this paper is to exemplify the power of SDA to determinewhat properties of measurements will yield estimates of unknown parameters to adesired precision, in a model with the complexity required to capture importantfeatures of the COVID-19 pandemic.

Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation