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 are expected to transmit the infection at a much higher rate than their quarantined counterparts. That is, under the lack of extensive random testing, the actual prevalence and incidence of the SARS-CoV-2 infection may be entirely different from that being reported. Thus, it is imperative that the information on the percentage of undetected (or unreported) cases be considered while estimating the parameters and forecasting the transmission dynamics of the epidemic.

In this paper, we have developed a new version of the basic susceptible-infected-removed (SIR) compartmental model, called the susceptible-infected (quarantined/ free) -recovered-deceased [SI(Q/F)RD] model, to incorporate the impact 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 Gibbs sampling procedure. As a demonstration, the proposed methodology is implemented to forecast the COVID-19 transmission in California and Florida.