Identifiability of parameters in mathematical models of SARS-CoV-2 infections in humans

Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of the parameter estimates to the noise in the data, we developed a novel two-patch within-host mathematical model that considered the infection of both respiratory tracts and assumed that the viral load in the lower respiratory tract decays in a density dependent manner and investigated its ability to match population level data. We proposed several approaches that can improve practical identifiability of parameters, including an optimal experimental approach, and found that availability of viral data early in the infection is of essence for improving the accuracy of the estimates. Our findings can be useful for designing interventions.