Table 1 Model parameters. These parameters were derived by Conway et al. [37, 49] using a range of studies and the package [50], with further details available in Ref. [51]. Note that the age brackets for probabilities of symptomatic infection, relative infectiousness once infectious, and susceptibility to becoming infected upon contact with an infected individual correspond to [0, 5, 10, 15, 20, 25, 30, 35,40, 45, 50, 55, 60, 65, 70, 75, 80]
From: Modelling the impact of hybrid immunity on future COVID-19 epidemic waves
Parameter: description | Value |
|---|---|
\(\mu _{\text {AZ1}}^{0}\): \(\log _{10}\) of the mean neutralising antibody titre after the first dose of AstraZeneca (no infection) [used in Eq. (1)] | -0.530 |
\(\mu _{\text {AZ2}}^{0}\): \(\log _{10}\) of the mean neutralising antibody titre after the second dose of AstraZeneca (no infection) [used in Eq. (1)] | -0.120 |
\(\mu _{\text {PB2}}^{0}\): \(\log _{10}\) of the mean neutralising antibody titre after the second dose of Pfizer (no infection); also the mean titre after one AstraZeneca dose and one infection [used in Eq. (1)] | 0.154 |
\(\mu _{\text {B}}^{0}\): \(\log _{10}\) of the mean neutralising antibody titre after the first mRNA booster dose (both with and without infection); also the mean titre after two AstraZeneca doses and one infection [used in Eq. (1)] | 0.323 |
\(\mu _{U}^{0}\): \(\log _{10}\) of the mean neutralising antibody titre after infection whilst unvaccinated [used in Eq. (1)] | 0 |
\(\sigma\): standard deviation of the \(\log _{10}\) of neutralising antibodies across the population | 0.465 |
\(c_{h}\): midpoint of logistic function Eq. (5) of protection against hospitalisation | -1.22 |
\(c_{d}\): midpoint of logistic function Eq. (5) of protection against death | -1.18 |
\(c_{\xi }\): midpoint of logistic function Eq. (5) of protection against acquisition | -0.472 |
\(c_{\tau }\): midpoint of logistic function Eq. (5) of protection against transmission | 0.0295 |
\(c_{q}\): midpoint of logistic function Eq. (5) of protection against symptomatic disease | -0.644 |
\(\log \left( k\right)\): governs the logistic curve steepness relating antibodies to protection against disease outcome [c.f. Eq. (5)] | 1.69 |
\(k_{a}\): decay rate of neutralising antibodies [c.f. Eq. (2)] | 0.00824 |
\(\log _{10}\left( f_{\text {Omicron}}\right)\): \(\log _{10}\) of the fold change in neutralising antibody titre between Delta and Omicron (BA1-like) [c.f. Eq. (4)] | -0.692 |
\(\log _{10}\left( f_{\text {Omicron-escape}}\right)\): \(\log _{10}\) of the fold change in neutralising antibody titre between Delta and the BA4/5-like immune escape variant [c.f. Eq. (4)] | -1.18 |
baseline age-group specific probability of symptomatic infection if infected | [0.29, 0.29, 0.21, 0.21, 0.27, 0.27, 0.33, 0.33, 0.4, 0.4, 0.49, 0.49, 0.63, 0.63, 0.69, 0.69, 0.69] |
baseline age-group specific relative infectiousness once infected | [0.799, 0.688, 0.675, 0.756, 0.918, 0.965, 0.947,0.932, 0.934, 0.940, 0.954, 0.982, 1.0, 0.998, 0.990, 0.974, 0.944] |
baseline age-group specific susceptibility to becoming infected upon contact with an infected individual | [0.301, 0.367, 0.433, 0.527, 0.764, 0.924, 0.983, 0.974, 0.932, 0.915, 0.929, 0.962, 1.0, 0.972, 0.882, 0.824, 0.802] |
\(R_{0}\) ratio between the original Omicron variant (BA1/2-like) and the BA4/5-like immune escape variant (the added transmissibility of the immune escape variant) | 1.3 |