Fig 1.
A) Typical course of an acute infection, e.g., influenza A virus or SARS-CoV-2, where the viral load initially increases (growth, up-slope), peaks, and decreases (clearance, down-slope). Viral load data is usually collected post-symptom onset (red dots). B) Example of SARS-CoV-2 data collection that starts 5 to 7 days post infection (from Wolfel et al. [3]). Filled red circles are viral load measurements above the limit of detection (horizontal dashed line), non-filled circles are below the limit of detection. The vertical dotted line represents the time of symptom onset as reported in [26]. [Created with BioRender.com].
Fig 2.
Schematic illustration of the refractory cell model.
A susceptible target cell, T, is infected by virus, V, with the infection rate constant β. Infected cells in the eclipse phase, E, become actively virus-producing cells, I, with the transition rate constant k. Infected cells, I, produce virus with production rate constant π or die with degradation rate δ. Virus is cleared with clearance rate c. In the refractory cell model, in addition we also account for the innate immune response, which turns susceptible cells into refractory cells,R, with constant rate φ, which are in an antiviral state and refractory to infection. However, refractory cells can become susceptible to infection with constant rate ρ. [Created with BioRender.com].
Fig 3.
The best RCM fit to viral load measurements of the 25 selected individuals.
Filled circles are measurement points; non-filled circles are censored and below the detection limit (dotted grey line). We fixed population parameters (without allowing random effects) for the initial target cell population, T0 = 8×107 cells, initial eclipse cell population, E0 = 1 cell, transition rate out of the eclipse phase, k = 4 /day, and the virus clearance rate, c = 10 /day (see Table 1 and Table B in S2 Text for individual parameters, S1 Data for viral load measurements and model predictions).
Fig 4.
Predicted dynamics of virus, infected cells, refractory cells, and target cells using the population parameters (black line) and individual parameters (colored lines) throughout the course of infection predicted by the RCM using the best-fit population parameter estimates (see S1 Data for model predictions).
Table 1.
Parameters in the RCM viral dynamic model and their estimated population values.
Fig 5.
Correlation of population parameters in the refractory cell model.
The sample size gives the number of fits that fit the model equally well in the range of min (-LL) to min(-LL)+2. Correlations that are crossed are non-significant (p-value > 0.05). The plot has been generated with ggstatsplot [doi:10.21105/joss.03167].
Fig 6.
RMSEs for the RCM and three infection time cases.
Infection times (tinf) are re-estimated (triangle), infection times are known and set to zero (square), or infection times are set to zero and the VL peaks 5 dpi (circle). RMSEs are shown for different subsets of the full data set: A) 3 dpi, B) 5 dpi, C) 7 dpi, and D) post-peak. For each case, all model parameters were re-estimated (NONE fixed on the x-axis), or the indicated model parameters were fixed to the values estimated from the full course of the infection data set and the remaining parameters estimated (see Table 1). The dashed line represents the RMSE calculated from the best model fit using the full course of infection (see S1 Data for RMSE values).
Fig 7.
Population parameters estimates averaged over the four subsets of the full data set using the RCM.
The dotted line represents the population parameter estimated from the “full course of infection” data set. The gray shaded area represents 95% confidence intervals of the population parameter estimated from the “full course of infection” data set (Population parameters estimated from each data subset individually can be found in Fig B in S2 Text and S1 Data).
Fig 8.
Heatmap RMSEs calculated with the RCM and different combinations of population parameters.
A) RMSEs for different combinations of literature values. B) RMSEs for fixed infection rates from literature and estimated virus production rates. C) RMSEs for fixed virus production rates from literature and estimated infection rates. ◊ = the population parameters we estimated, x = values for β and/or π found in literature. Parameter values can be found in Table C in S2 Text. Note that the underlying heatmap is the same for A), B), and C), and it was calculated from fits to the post-peak viral load data set and assumed 5 days to reach peak viral load for each pair of β and π values indicated in the x and y-axes, respectively (see S1 Data for RMSE values).