Extending the Susceptible-Exposed-Infected-Removed (SEIR) model to handle the high false negative rate and symptom-based administration of COVID-19 diagnostic tests: SEIR-fansy

The false negative rate of the diagnostic RT-PCR test for SARS-CoV-2 has been reported to be substantially high. Due to limited availability of testing, only a non-random subset of the population can get tested. Hence, the reported test counts are subject to a large degree of selection bias. We consider an extension of the Susceptible-Exposed-Infected-Removed (SEIR) model under both selection bias and misclassification. We derive closed form expression for the basic reproduction number under such data anomalies using the next generation matrix method. We conduct extensive simulation studies to quantify the effect of misclassification and selection on the resultant estimation and prediction of future case counts. Finally we apply the methods to reported case-death-recovery count data from India, a nation with more than 5 million cases reported over the last seven months. We show that correcting for misclassification and selection can lead to more accurate prediction of case-counts (and death counts) using the observed data as a beta tester. The model also provides an estimate of undetected infections and thus an undereporting factor. For India, the estimated underreporting factor for cases is around 21 and for deaths is around 6. We develop an R-package SEIR-fansy for broader dissemination of the methods.