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

We demonstrate the ability of statistical data assimilation to identify the measurements required for accurate state and parameter estimation in an epidemiological model for the novel coronavirus disease COVID-19. Our context is an effort to inform policy regarding social behavior, to mitigate strain on hospital capacity. The model unknowns are taken to be: the time-varying transmission rate, the fraction of exposed cases that require hospitalization, and the time-varying detection probabilities of new asymptomatic and symptomatic cases. In simulations, we obtain accurate estimates of undetected (that is, unmeasured) infectious populations, by measuring the detected cases together with the recovered and dead - and without assumed knowledge of the detection rates. These state estimates require a measurement of the recovered population, and are tolerant to low errors in that measurement. Further, excellent estimates of all quantities are obtained using a temporal baseline of 112 days, with the exception of the time-varying transmission rate at times prior to the implementation of social distancing. The estimation of this transmission rate is sensitive to contamination in the data, highlighting the need for accurate and uniform methods of reporting. Finally, we employ the procedure using real data from Italy reported by Johns Hopkins. The aim of this paper is not to assign extreme significance to the results of these specific experiments \textit{per se}. Rather, we intend to exemplify the power of SDA to determine what properties of measurements will yield estimates of unknown model parameters to a desired precision - all set within the complex context of the COVID-19 pandemic.