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

To understand the observed SARS-COV-2 shedding dynamics we developed a viral infection model modifying previous models of virus dynamics (12, (35) (36) (37) . In this model, susceptible cells (S) are infected at rate by SARS-COV-2 (V). SARS-COV-2-infected cells (I) are cleared in two ways: (1) by an innate response with density dependent rate ! (13, 14) ; and (2) an acquired response with rate "# ! # ! $% ! mediated by SARS-COV-2-specific effector cells ( ). The exponent describes by how much the first death rate depends on the infected cell density. The Hill coefficient parameterizes the nonlinearity of the second response and allows for rapid saturation of the killing. Parameter defines the effector cell level by which killing of infected cells by is half maximal. SARS-COV-2 is produced at a rate and cleared with rate . In the model, SARS-COV-2-specific effector cells rise after stages from precursors cells ( '()…+ ). The first precursor cell compartment ( ) ) proliferates in the presence of infection with rate ) and differentiates into the effector cell at a per capita rate during each intermediate stage. Finally, effector cells die at rate # . The best instance of the model is expressed as a schematic (Fig. 1a) and here as a system of ordinary differential equations: (1)