Figure 1.
Conceptual overview of the framework.
Within-host models of infection dynamics in a spatially-structured respiratory tract composed of three linearly-connected compartments are used to estimate overall virus excretion (X) and pathogenicity (P). The parameters that differ per respiratory compartment (i) are the initial number of susceptible cells (S0,i), the viral clearance rate (χi), and the distribution coefficients of immunoglobulins of type A (IgA) and IgG (cai and cgi, respectively). The measures of virus excretion (X) and pathogenicity (P) in turn are used to estimate population-level transmission rate (βh), mortality rate (αh), and recovery rate (γh), which define the virus reproductive number (R). See Methods for more details.
Table 1.
Characteristics of the human respiratory tract.
Table 2.
Range of parameter estimates of the within-host models of infection dynamics.
Figure 2.
Output of within-host models is represented by curves. Black line: mean values across models; grey shaded area: standard deviation. Data points from empirical studies are represented by symbols. A. Viral shedding; B. Type I interferon; C. Cytotoxic T cells; D. Immunoglobulins of type A (IgA; triangles) and IgG (crosses). HI: hemagglutination inhibition.
Figure 3.
Optimal receptor binding affinity patterns.
Contour plots of influenza virus basic reproductive number R0 (color scales) are drawn when the affinity coefficients a2,3 (x axis) and a2,6 (y axis) are varied from 0 to 1. For all graphs, the initial number of susceptible cells differ per respiratory compartment to reflect the heterogeneities in abundance and distribution of epithelial cells with sialic acids with α2,3 or α2,6 linkage to galactose. The effect of heterogeneities in viral clearance rates (χi) and in the contribution of pathogenicity in each respiratory compartment (Pi) to the overall virus pathogenicity (P) on the virus R0 is determined, when either non-linear or linear functions link within-host model output of viral excretion (X) and pathogenicity (P) to between-host model parameters. For panels A to D, χ1> χ2> χ3; for panels E and F, χ1 = χ2 = χ3. For panels A, C and E, P = ∑ Pi; for panels B, D and F, P = P1+102 P2+103 P3. For panels A, B, E and F, non-linear functions link within-host model output to between-host model parameters; for panels C and D, linear functions link within-host model output to between-host model parameters.
Figure 4.
Optimal patterns of tissue tropism and associated morbidity and mortality burdens.
Contour plots of influenza virus reproductive number (color scales) in an immunologically naïve population (R0; A) and in a partially-immune population (Re; B) are drawn when the infectivity rates β2 (x axis) and β1 (y axis) are varied. In all cases, the infectivity rate β3 is kept constant and equals the lowest infectivity rate in the explored range (10−10 h−1). Note that the optimal tissue tropism differs in an immunologically naïve and in a partially-immune population. C. The total number of cases per 10 000 individuals (light grey bars) and the number of fatal cases per 100 000 individuals (black bars) are represented for the influenza virus with optimal tissue tropism in an immunologically naïve population (year 0) and for the influenza virus with optimal tissue tropism in a partially-immune population (year 1). Their respective case-fatality rate is indicated by a dark grey diamond. D. The percentage reduction in pathogenicity in the bronchiolar compartment (P2) of the influenza virus with optimal tissue tropism in a partially-immune population is shown in a naïve individual and in an individual with pre-existing immunity in year 1 compared to that of the influenza virus with optimal tissue tropism in an immunologically naïve population (year 0).
Figure 5.
Relationship between optimal β2/β1 ratio and Si,2/Si,1 ratio in the absence of pre-existing immunity.
The optimal infectivity rate in the bronchiolar compartment (β2) is smaller than the optimal infectivity rate in the tracheo-bronchial compartment (β1) provided that the initial number of susceptible cells in the bronchiolar compartment (Si,2) is larger than the initial number of susceptible cells in the tracheo-bronchial compartment (Si,1).