Model Structure

The LMIC reports are generated using an age-structured SEIR model. The developed model is an extension of the model used in our previous report (see Report 12 and the related publication) and the source code for the model can be found at https://github.com/mrc-ide/squire. In this model, the infectious class is divided into different stages reflecting progression through different disease severity pathways. These compartments are:


Given initial inputs of hospital/ICU bed capacity and the average time cases spend in hospital, the model dynamically tracks available hospital and ICU beds over time. Individuals newly requiring hospitalisation (either a hospital or ICU bed) are then assigned to either receive care (if the relevant bed is available) or not (if maximum capacity would be exceeded otherwise). Whether or not an individual receives the required care modifies their probability of dying.

In more recent model fitting and scenario projections, we model the roll out of vaccinations. For this work we use the extended version of the above model that was used in our previous reports on vaccination (see Report 33 and the related publication) and the source code for the model can be found at https://github.com/mrc-ide/nimue.

This particular model is an extension to nimue that incorporates booster doses (source code here, which is liable to change). For more information see this vignette.

Fitting Procedure

To calibrate our model to the deaths (or excess-mortality) we first simulate random draws from pre-define distributions on our models parameters (defined below). Then we optimise the \(R_t\) values over defined period to get a close fit to the death curve. Please see this vignette for a more technical overview. These parameter draws and \(R_t\) trajectories are then used to simulate our scenarios and infection curves.

Interventions

We represent any interventions as changes to the overall \(R_t\) of the epidemic, which we define as the reproductive number in the absence of vaccine or disease derived immunity. We allow this value to vary every 2 weeks, which represents changes to mobility, interventions, and changes in transmission due to variants.

Variant Adjustments

We make adjustments for the non-transmission effects of variants. These are mainly immune-escape from vaccine and infection derived protection. For reduced vaccine efficacies we scale these values over a period where the new variant is deemed to have become dominant. For the escape from natural protection, we increase the rate of loss of immunity over this period. The timings of these periods are determined using sequence data from NextStrain and are reported on each countries page, with caveats.

Uncertainty

We allow these parameters to vary across each sample, this allow us to incorporate our uncertainty in these values.

Vaccine Efficacy

The table below shows the central VE estimates by vaccine type (taken from the appendix of Watson et al.):

Vaccine Type Dose Variant Protection Against Infection Protection Against Hospitalisation
mRNA Partial Wild 0.63 0.83
mRNA Full Wild 0.86 0.95
mRNA Partial Delta 0.36 0.83
mRNA Full Delta 0.88 0.93
Johnson&Johnson Full Wild 0.66 0.83
Johnson&Johnson Full Delta 0.5 0.74
Adenovirus Partial Wild 0.64 0.79
Adenovirus Full Wild 0.77 0.94
Adenovirus Partial Delta 0.3 0.71
Adenovirus Full Delta 0.67 0.92
Whole Virus Partial Wild 0.5 0.5
Whole Virus Full Wild 0.67 0.79
Whole Virus Partial Delta 0.1 0.14
Whole Virus Full Delta 0.6 0.7
Subunit Partial Wild 0.54 0.83
Subunit Full Wild 0.86 0.96
Subunit Partial Delta 0.3 0.68
Subunit Full Delta 0.71 0.86
mRNA Partial Omicron 0 0.464
mRNA Full Omicron 0.136 0.52
Johnson&Johnson Full Omicron 0.0774 0.414
Adenovirus Partial Omicron 0 0.397
Adenovirus Full Omicron 0.104 0.514
Whole Virus Partial Omicron 0 0.0783
Whole Virus Full Omicron 0.0929 0.391
Subunit Partial Omicron 0 0.38
Subunit Full Omicron 0.11 0.481

WIP

These parameters are then used to generate waning efficacy curves using a simulated antibody decay which the models vaccine parameters are then fitted to. Uncertainty is incorporated by drawing from a Beta distribution centred on those fitted parameter values. Which vaccine type to model is uniformly selected from all vaccines reported to have been used in the country.

WIP

Variant Specific

Immune-Escape for Naturally Aquired Immunity:
Variant Distribution 95% CI
Delta Beta(1.014, 2) 0.0133, 0.843
Omicron Beta(2.54, 2) 0.149, 0.922
Omicron Sub-Variant Beta(1.014, 2) 0.0133, 0.843
Multiplier on the Probablity of Hospitalisation:
Variant Distribution 95% CI
Delta Log-Normal(ln(1.45), 0.15) 1.08, 1.95
Omicron Log-Normal(ln(0.59), 0.08) 0.504, 0.69
Omicron Sub-Variant Log-Normal(ln(1), 0.08) 0.855, 1.17
Multiplier on the Probablity of Requiring ICU:
Variant Distribution 95% CI
Delta Log-Normal(ln(1), 0.08) 0.855, 1.17
Omicron Log-Normal(ln(0.34), 0.45) 0.141, 0.821
Omicron Sub-Variant Log-Normal(ln(1), 0.08) 0.855, 1.17

Baseline Infection Fatality Ratio

To maintain consistency within the age-structured IFR, we simulate a single value for all ages and scale between lower, central, and upper estimates with this value. These values are:

Infection Fatality Ratio (%) (assuming healthcare capacity unmet)
Age-Group Central Lower Upper
0 - 5 0 0 0.03
5 - 10 0.01 0 0.06
10 - 15 0.01 0 0.11
15 - 20 0.02 0 0.18
20 - 25 0.03 0 0.3
25 - 30 0.04 0 0.46
30 - 35 0.06 0.01 0.71
35 - 40 0.1 0.01 1.03
40 - 45 0.16 0.02 1.47
45 - 50 0.24 0.03 2.03
50 - 55 0.38 0.05 2.74
55 - 60 0.6 0.1 3.64
60 - 65 0.94 0.18 4.79
65 - 70 1.47 0.35 6.27
70 - 75 2.31 0.65 8.21
75 - 80 3.61 1.21 10.8
80+ 8.82 4.18 19

Calculated from IFR in Report 34. To produce this IFR we scale the probabilities of hospitalisation, severity, and death given severity, with defaults:

Age-Group Probability of Hospitalisation (%), given infection Probability of Requiring ICU (%), given hospitalisation
0 - 5 0.0841 18.1
5 - 10 0.118 18.1
10 - 15 0.166 18.1
15 - 20 0.234 13.7
20 - 25 0.329 12.2
25 - 30 0.463 12.3
30 - 35 0.65 13.6
35 - 40 0.915 16.1
40 - 45 1.29 19.7
45 - 50 1.81 24.2
50 - 55 2.54 28.9
55 - 60 3.58 32.7
60 - 65 5.03 33.7
65 - 70 7.08 30.9
70 - 75 9.95 24.4
75 - 80 14 16
80+ 23.3 5.71
Source: Salje et al. Salje et al.

The probability of death without healthcare is given by:

Probability of Death without treatment
Severity Distribution 95% CI
Requires ICU Beta(44.2, 2.33) 0.872, 0.992
Does not Require ICU Beta(124, 124) 0.438, 0.562

This values are informed by expert opinion.

Please note that this IFR is representative of Wild-type COVID-19 in our model.

The mean duration of natural immunity is assumed to be distributed by \(\mathrm{Gamma}(20, 4/73)\) with 95% CI of 223, 541 days.

Fixed Model Parameters

The parameter table below summarises the fixed parameters estimates incorporated in the squire package.

Parameter Value Reference
Mean Incubation Period 4.6 days Estimated to be 5.1 days (Linton et al.; Li et al. The last 0.5 days are included in the I_MILD and I_CASE states to capture pre-symptomatic infectivity
Generation Time 6.75 days Bi et al
Mean Duration in I_MILD 2.1 days Incorporates 0.5 days of infectiousness prior to symptoms; with parameters below ~95% of all infections are mild. In combination with mean duration in I_CASE this gives a mean generation time as above
Mean Duration in I_CASE 4.5 days Mean onset-to-admission of 4 days. Values in the literature range from 1.2 to 12 days. Includes 0.5 days of infectiousness prior to symptom onset
Mean Duration of Hospitalisation for non-critical Cases (I_HOSP) if survive 9 days Median value from five studies (Sreevalsan-Nair et al., Haw et al., Hawryluk et al., Oliveira et al., South African COVID-19 Modelling Consortium). Range from 8-15 days.
Mean Duration of Hospitalisation for non-critical Cases (I_HOSP) if die 9 days As above
Mean duration of Critical Care (I_ICU) if survive 14.8 days Mean duration in ICU of 13.3 days Pritchard et al.. Ratio of duration in critical care if die: duration in critical care if survive of 0.75 and 60.1% probability of survival in ICU (ICNARC report, from UK data, 16 October 2020)
Mean duration of Critical Care (I_ICU) if die 11.1 days Mean duration in ICU of 13.3 days Pritchard et al.. Ratio of duration in critical care if die: duration in critical care if survive of 0.75 and 60.1% probability of survival in ICU (ICNARC report, from UK data, 16 October 2020)
Mean duration of Stepdown post ICU (I_Rec) 3 days Working assumption based on unpublished UK data
Mean duration of hospitalisation if require ICU but do not receive it and die 1 day Working assumption
Mean duration of hospitalisation if require ICU but do not receive it and survive 7.4 days Working assumption (Half duration of ICU and survive)
Mean duration of hospitalisation if require Oxygen but do not receive it and die 4.5 days Working assumption (Half duration of Oxygen and die)
Mean duration of hospitalisation if require Oxygen but do not receive it and survive 4.5 days Working assumption (Half duration of Oxygen and survive)


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