How reliable are estimates of key parameters in viral dynamic models?

Mathematical models of viral infection have been developed and fit to data to gain insight into disease pathogenesis for a number of agents including HIV, hepatitis C and B virus. However, for acute infections such as influenza and SARS-CoV-2, as well as for infections such as hepatitis C and B that can be acute or progress to being chronic, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the exponential phase of viral growth, i.e., when most transmission events occur. Missing data may make estimation of the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. Here, we evaluated the reliability of estimates of key model parameters when viral load data prior to the viral load peak is missing. We estimated the time from infection to peak viral load by fitting non-linear mixed models to a dataset with frequent viral RNA measurements, including pre-peak. We quantified the reliability of estimated infection times, key model parameters, and the time to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. We find a lack of data in the exponential growth phase underestimates the time to peak viral load by several days leading to a shorter predicted exponential growth phase. On the other hand, having an idea of the time of infection and fixing it, results in relatively good estimates of dynamical parameters even in the absence of early data.