Fig 1.
Results of model fitting for virological and macrophage data.
Data are presented by solid circles for HP and solid triangles for LP strains. As mentioned in the Materials and methods, the data were adopted from [18], and macrophage data represented the sum of all three subpopulations of macrophages (i.e., MR + M1 + M2). We performed 6000 model simulations based on 6000 posterior samples from the posterior distributions of estimated parameters (see S1 Fig for the H1N1 viurses and S2 Fig for the H5N1 viruses). (A, B) show a 95% prediction interval (shaded area) of viral load and macrophage for HP (red) and LP (green) strains of the H1N1 viruses, respectively. Solid lines are illustrative viral and macrophage trajectories. (C, D) show the data and model predictions of viral load and macrophage dynamics for HP and LP strains of the H5N1 viruses, respectively.
Fig 2.
Prediction of tissue damage for H1N1 viruses.
The violin plots (coloured) and boxplots (white) give the density and the median and extrema of the predicted quantity. (A) model prediction of the maximal epithelium loss for the HP (yellow) and LP (green) strains. (B) model prediction of the cumulative level of dead cells during the infection for both strains. ***p<0.001. For calculation formulas see Eqs 11 and 12 in the Materials and methods. All estimations are computed using 6000 posterior samples from model fitting. The estimations for the H5N1 viruses are given in S3 Fig.
Fig 3.
Comparison of estimated model parameters between HP and LP strains of the H1N1 viruses.
Histograms show the frequency of the ratios of estimated HP parameters over paired LP model parameters and are normalised to [0, 1]. The ratios are presented by distributions of 6000 samples because they are generated by 6000 posterior parameter values. The cumulative density functions (CDFs) are given by the solid lines, and the dashed lines indicate ratios = 0. All ratios are log10-scaled, such that ratios > 0 (dark green) suggest greater values of the HP parameters. Fig (A, B, C) show the ratios of viral infectivity, and interferon production rate from infected cells and activated macrophages, respectively. Fig (D, E, F) show the ratios of infection-induced macrophage recruitment rate, macrophage-mediated virus clearance rate and antibody neutralisation rate, respectively. The model parameter comparison for the H5N1 viruses is given in S4 Fig.
Fig 4.
Correlations between estimated model parameters and tissue damage.
Partial rank correlation coefficients (PRCC) are calculated with respect to (A) the ratio of max epithelium loss between HP and LP strains, and (B) the ratio of the cumulative dead cells between HP and LP strains of H1N1 viruses. The two red dashed lines represent the statistically insignificant values of PRCC. Calculations are based upon 6000 posterior samples from model fitting. PRCC analysis for H5N1 viruses is given in S5 Fig.
Fig 5.
The relative contribution of macrophages to viral clearance in the HP and LP strains of the H1N1 viruses.
The prediction interval (PI) is calculated based on the 6000 posterior samples from model fitting. The median trajectory is indicated by the black curve. The predictions for the H5N1 viruses are given in S6 Fig.
Fig 6.
Parameters driving tissue damage for the HP H1N1 virus.
Fig (A, B, C) give the sensitivity analyses of the impact of β, qFI and sV on maximal epithelium loss. Fig (D, E, F) show the impact of the same three model parameters on the cumulative dead cells. The baseline values for the parameters were chosen so that the median value of the maximal percentage of tissue damage (panels A, B, C) or the cumulative dead cells (panels D, E, F) corresponds to the value from our main analysis (Fig 2A and 2B respectively). Parameters driving tissue damage for the LP H1N1 virus are given in S7 Fig.
Fig 7.
A model diagram of immune response to influenza viral infection.
A detailed model (Eqs 1–10)) description is given in Materials and Methods. Plus (+) superscript indicates the promotion of a biological process, and minus (−) superscript means the inhibition of a process. In brief, influenza virus (V) turns susceptible epithelium cells (T) into eclipse-phase infected cells (L) which in turn, become infected cells (I) that actively produce new viruses. The virus also infects resting macrophages (MR) and turns them into pro-inflammatory macrophages (M1). Viruses are cleared through the MR macrophage ingestion and antibody neutralisation. Infected cells (I) and M1 macrophages produce interferons (F) that turns susceptible cells (T) into refractory cells (R). The refractory cells (R) lose protection and turn back to T. Infected cells (I) are killed and become dead cells (D) through interferons- and CD8+ T cells-mediated clearance. M1 macrophages clear dead, which facilitates the conversion of MR to anti-inflammatory M2 macrophages. Both activated M1 and M2 macrophages convert back to MR macrophages at certain rates. For clarity, flows depicting the natural decay of activated macrophages (M1 and M2), virus (V) and interferons (F), and the replenishment of resting macrophages (MR) and target cells (T) are not shown in the diagram. The figure was created with BioRender.com.