We investigated the effect on the dynamics of the model when the parameter values were varied. The virus peak, the time when the peak occurred, the IFN peak, and the percentage of cell death were recorded as each of the parameter values in the model was varied (Fig.
A2 and
A3). The “average” estimates for the parameters in Table
2 were used as baseline values. For the rest of the parameters, the values reported in Table
1 were used as baseline values. The values for the estimated parameters (Table
2) were varied from a factor of 1/10 to 10 times their estimated values (Fig.
A2). On the other hand, the values for the preset parameters (Table
1) were varied from 50% to 150% of their baseline values (Fig.
A3). The uncertainty expected in the estimates in Table
2 was the main reason for having different factors for the parameters in Fig.
A2 and
A3. Both the transmission parameter, β, and the virus production,
p, have a strong effect on all the dynamics of the model, increasing cell death and virus and IFN peaks and decreasing the time for the virus peak (Fig.
A2). A similar effect was observed when the parameter
m was varied (Fig.
A3). The IFN efficiency, φ, and IFN production,
q, have an effect on only the IFN peak and the percentage of cell death (Fig.
A2). The initial virus shedding,
V 0, seems to have any effect on only the time when the virus peak occurs (Fig.
A2). The eclipse phase period, 1/
k 1, determines when the virus peak occurs, while the infectious period, 1/δ, has an effect on the value of the peak (Fig.
A3). Similarly, the virus clearance rate,
c, has a strong effect on the virus peak, but it also affects the IFN peak and the percentage of cell death (Fig.
A3). The duration of the prerefractory state, 1/
a, has a negative effect on all the dynamics of the model (Fig.
A3). The IFN clearance rate,
d, has a strong effect on the IFN peak and a mild effect on the percentage of cell death (Fig.
A2). The IFN-reduced production,
n, seems to affect only the amount of IFN at its peak (Fig.
A3).
The value of the total number of epithelial cells,
T 0, scales the rates of virus and IFN production per cell,
p and
q, respectively. To show this, following a method described previously (
45), let (
T,
E 1,
W,
E 2,
R,
I,
V,
F) be the solution for system 1 with initial condition (
T 0, 0, 0, 0, 0, 0,
V 0, 0). Then, it can be easily determined that (T̃, Ẽ
1, W̃, Ẽ
2, R̃, Ĩ, Ṽ, F̃) = (σT, σE
1, σW, σE
2, σR, σI, V, F) is the solution of system 1 with the new parameters p̃ = (1/σ)p and q̃ = (1/σ)q and for the initial condition (σT
0, 0, 0, 0, 0, 0,
V 0, 0).