Potency and timing of antiviral therapy as determinants of duration of SARS CoV-2 shedding and intensity of inflammatory response

Ashish Goyal; E. Fabian Cardozo-Ojeda; Joshua T Schiffer

We developed a series of ordinary differential equations to fit to the viral load data (Fig. 1a , Methods and Materials). The equations capture the coupled interactions of susceptible cells, infected cells, SARS CoV-2 and a mounting immune response. In keeping with the standard viral dynamics model (11, 12) , virus enters susceptible cells and converts them to infected dells which then produce virus at a fixed rate. Based on model fitting, we included two immune responses. The first accounts for the rate of infected cell elimination by the innate immune system and is governed by an exponent; in keeping with prior research, we refer to this as the density-dependent immune response (13, 14) . The second phase is a slower cytolytic response in which per cell killing rate saturates once the total number of effector cells exceeds a certain level. We model this with stages of presumed effector cell precursors which differentiate at rate q as a method to calibrate timing.