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1.
Figure 3

Figure 3. From: Critical immune and vaccination thresholds for determining multiple influenza epidemic waves.

Contour curve for Rn(f1, f2) = 1. The points (f1, f2) on the curve are the critical immune vectors.

Laura Matrajt, et al. Epidemics. ;4(1):22-32.
2.
Figure 2

Figure 2. From: Critical immune and vaccination thresholds for determining multiple influenza epidemic waves.

Contour curve for Rf (f1, f2) = 1. The points (f1, f2) on the curve are the critical vaccination vectors.

Laura Matrajt, et al. Epidemics. ;4(1):22-32.
3.
Figure 7

Figure 7. From: Critical immune and vaccination thresholds for determining multiple influenza epidemic waves.

Sensitivity analysis for the vaccine efficacies considered. The vaccine efficacies were taken from a uniform distribution of length 0.2 centered around the values used. Each vaccine efficacy was drawn independently. The results are quite robust with respect to these parameters.

Laura Matrajt, et al. Epidemics. ;4(1):22-32.
4.
Figure 5

Figure 5. From: Critical immune and vaccination thresholds for determining multiple influenza epidemic waves.

Analysis for the second wave of pandemic H1N1 influenza in London and the West Midlands. The red mark and confidence intervals represents the fraction of children and adults naturally immune (people who were infected during the first wave).

Laura Matrajt, et al. Epidemics. ;4(1):22-32.
5.
Figure 1

Figure 1. From: Critical immune and vaccination thresholds for determining multiple influenza epidemic waves.

Surfaces representing all the eigenvalues of the next generation matrix for R0 = 1.6. All the eigenvalues of the matrix but two are zero (plotted in yellow). The ones that are non-zero are plotted above in red and blue. The green plot corresponds to the plane z = 1. Here, the blue surface corresponds to the effective reproduction number with vaccination, Rf (f1, f2).

Laura Matrajt, et al. Epidemics. ;4(1):22-32.
6.
Figure 4

Figure 4. From: Critical immune and vaccination thresholds for determining multiple influenza epidemic waves.

The shaded regions indicate the intermediate regions for a specific R0, (where R0 ∈ [1.2, 1.8]) that is, the region where the threshold for a mixture of vaccine-induced immunity and natural immunity should lie. The level of combined immunity (vaccine-induced and naturally-acquired immunity) at the end of winter 2010, calculated from on [23] and [27], is given by the dotted square S.

Laura Matrajt, et al. Epidemics. ;4(1):22-32.
7.
Figure 8

Figure 8. From: Critical immune and vaccination thresholds for determining multiple influenza epidemic waves.

Sensitivity analysis for the recovery rates for children and adults considered. Each recovery rate was independently taken from a uniform distribution of length 0.2 centered around the values used. Only those pairs for which the R0 fell in one of the following intervals were used: 1.15 < R0 < 1.25, or 1.35 < R0 < 1.45, or 1.55 < R0 < 1.65 or 1.75 < R0 < 1.85. The results are very robust with respect to these parameters.

Laura Matrajt, et al. Epidemics. ;4(1):22-32.
8.
Figure 6

Figure 6. From: Critical immune and vaccination thresholds for determining multiple influenza epidemic waves.

Sensitivity analysis for the contact rates taken from a uniform distribution of length 0.2, centered at the value of the cij used. The contact rates were taken independently but only the triplets that gave 1.15 < R0 < 1.25, or 1.35 < R0 < 1.45, or 1.55 < R0 < 1.65 or 1.75 < R0 < 1.85 and where c11 > c12 and c11 > c22 were considered. The results are generally robust under this sensitivity. As long as R0 < 1.6, all the runs lie below the dotted rectangle, indicating that a recurrent epidemic wave is very unlikely. For R0 = 1.6, most of the curves intersect the rectangle, suggesting that a following wave is plausible. For R0 = 1.8 most of the curves overlap with the rectangle or lie above the rectangle, indicating that a third wave would be very likely. The black curve indicates the critical vaccination curve used in the analysis.

Laura Matrajt, et al. Epidemics. ;4(1):22-32.

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