Estimate of the development of the epidemic reproduction number Rt from Coronavirus SARS-CoV-2 case data and implications for political measures based on prognostics

Sahamoddin Khailaie; Tanmay Mitra; Arnab Bandyopadhyay; Marta Schips; Pietro Mascheroni; Patrizio Vanella; Berit Lange; Sebastian Binder; Michael Meyer-Hermann

The inverse of R4 is the duration for which the infected individuals with mild symptoms and not requiring hospitalization, remain infectious after their disease onset. To estimate this, we have made use of one study with nine young patients with no underlying health conditions, where the excretion dynamics of reproductive viruses (Woelfel et al. 2020 ) from samples of the throat and sputum were examined. This study suggests active virus replication in the upper respiratory tract in the earlier phase of the disease following onset of symptoms. RT-PCR tests result in detectable viral sub-genomic messenger RNAs (sgRNA) in swabs from throat in the first 5 days after symptoms onset (In Figure 1 (d) of Woelfel et al. 2020 , the throat swab cultures are positive up to the 4 th day, which the authors mark as sample of 4/5 days). However, we note that active virus is found in the sputum until day 8 for these mildly ill cases. Accounting for some variations, we assume that patients with minor illnesses not requiring hospitalization are infectious for 6 days following disease onset, which results in a value of 6 days for 1/R4. For such individuals, to calculate the median value of R4, we neglect a potentially longer period of possible infections transmitted via the sputum, this mode of transmission being especially meaningful in a hospital setting. For our analysis, we have considered a range of 4 -14 days for 1/R4.