A new extension of state-space SIR model to account for Underreporting – An application to the COVID-19 transmission in California and Florida

In the absence of sufficient testing capacity for COVID-19, a substantial number of infecteds are expected to remain undetected. Since the undetected cases are not quarantined, they can be expected to transmit the infection at a much higher rate than their quarantined counterparts. That is, in the absence of extensive random testing, the actual prevalence and incidence of the SARS-CoV-2 infection can be significantly higher than that being reported. Thus, it is imperative that the information on the percentage of undetected (or unreported) cases be incorporated in the mechanism for estimating the key epidemiological parameters, like rate of transmission, rate of recovery, reproduction rate, etc., and hence, for forecasting the transmission dynamics of the epidemic. In this paper, we have developed a new dynamic version of the basic susceptible-infected-removed (SIR) compartmental model, called the susceptible-infected (quarantined/ free) - recovered- deceased [SI(Q/F)RD] model, to assimilate the impact of the time-varying proportion of undetected cases on the transmission dynamics of the epidemic. Further, we have presented a Dirichlet-Beta state-space formulation of the SI(Q/F)RD model for the estimation of its parameters using posterior realizations from the Gibbs sampling procedure. As a demonstration, the proposed methodology has been implemented to forecast the COVID-19 transmission in California and Florida. Results suggest significant amount of underreporting of cases in both states. Further, posterior estimates obtained from the state-space SI(Q/F)RD model show that average reproduction numbers associated with the undetected infectives [California: 1.464; Florida: 1.612] are substantially higher than those associated with the quarantined infectives [California: 0.497; Florida: 0.359]. The long-term forecasts of death counts show trends similar to those of the estimates of excess deaths for the comparison period post training data timeline.