COVID-19 Scenario Analysis Tool

MRC Centre for Global Infectious Disease Analysis, Imperial College London

Note: Simulation outputs should not be interpreted as predictions

Research

This research is funded by The Wellcome Trust and with UK aid from the UK government.

The COVID-19 Scenario Analysis Tool enables users quickly and easily to generate calibrated forward scenarios of the COVID-19 epidemic in low- and middle-income countries in order to facilitate health planning.

This tool allows the user to make projections of the prevalence of infections each day and the expected number of people requiring hospitalisation and critical care facilities. The relative benefits of different scenarios can be compared with metrics including health system capacity (maximum number of beds and critical care beds needed compared to those available), the peak of the epidemic, and the total projected deaths up to 1st February 2021. The model is automatically re-calibrated daily to the cumulative COVID-19 deaths reported up to the previous day, obtained from the European Centres for Disease Control.

The impact of interventions that have been put in place is captured using data from the Oxford Coronavirus Government Response Tracker. Note that there is a delay between interventions being implemented and them appearing in this database. We currently make assumptions about the efficacy of these interventions; work is ongoing to incorporate movement data to better estimate these effects.

The user can compare each scenario to the projected impact of an unmitigated epidemic (the counterfactual of no intervention having been implemented). For countries with no intervention yet implemented, the user can input start and end dates for an intervention to explore the effectiveness of reducing transmission. For countries where interventions have already been implemented, the user can explore the impact of keeping the interventions in place for different timescales, and of reducing or increasing their effectiveness over this period. After the first intervention is relaxed, the user can explore levels of continued transmission reduction to explore potential “exit” strategies.

The tool is based on a deterministic, age-structured SEIR model incorporating explicit passage through disease severity settings and healthcare. Details of the model and its baseline parameters are given below. This builds on the work reported in the MRC Centre for Global Infectious Disease Analysis (MRC GIDA) Report 12 – “The global impact of COVID-19 and strategies for mitigation and suppression”. A parallel R package for the equivalent stochastic model – squire – is available from the MRC Centre for Global Infectious Disease Analysis GitHub site for academic purposes.

Model Structure

The COVID-19 Scenario Analysis Tool uses an age-structured SEIR model, with the infectious class divided into different stages reflecting progression through different disease severity pathways. These compartments are:

S = Susceptibles
E = Exposed (Latent Infection)
IMild = Mild Infections (Not Requiring Hospitalisation) – including asymptomatic infection
ICase = Infections that will subsequently require hospitalisation
IHospital = Hospitalised Infection (Requires General Hospital Bed)
IICU = Hospitalised Infection in critical care/ICU (Requires critical care/ICU Bed)
IRec = Hospitalised Infection Recovering from critical care/ICU Stay (Requires General Hospital Bed)
R = Recovered
D = Dead

Given initial inputs of hospital/ICU bed capacity and the average time cases spend in hospital, the model dynamically tracks available general hospital and ICU beds over time.

Individuals newly requiring hospitalisation (either a general hospital or ICU bed) are then assigned to either receive appropriate 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.

Model Parameters

The parameter table below summarises the current best estimates incorporated in the package. These will be updated as our understanding of the epidemic develops.

Parameter Value Reference
Basic reproductive number, R03MRC GIDA Report 13
Mean Incubation Period4.6 daysMRC GIDA Report 9; 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 Time6.75 daysMRC GIDA Report 9; Bi et al. 2020
Mean Duration in IMild2.1 daysIncorporates 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 ICase4.5 daysMean onset-to-admission of 4 days from unpublished UK data. Includes 0.5 days of infectiousness prior to symptom onset
Mean Duration of Hospitalisation for non-critical Cases (IHospital) if survive9.5 daysBased on unpublished UK data
Mean Duration of Hospitalisation for non-critical Cases (IHospital) if die7.6 daysBased on unpublished UK data
Mean duration of Critical Care (IICU) if survive11.3 daysBased on UK data adjusted for censoring
Mean duration of Critical Care (IICU) if die10.1 daysBased on UK data adjusted for censoring
Mean duration of Stepdown post ICU (IRec)3.4 daysBased on unpublished UK data
Mean duration of hospitalisation if require critical care (ICU) but do not receive it1 dayWorking assumption
Probability of dying in critical care0.5Based on UK data
Probability of death if require critical care but do not receive it0.95Working assumption based on expert clinical opinion
Probability of death if require hospitalisation but do not receive it0.6Working assumption based on expert clinical opinion

HIC – high-income country; IFR – infection fatality ratio; LIC – low-income country; LMIC – lower middle-income country.

Age-Specific Parameters

Age-Group Proportion of Infections Hospitalised Proportion of hospitalised cases requiring critical care Proportion of non-critical care cases dying
0 to 40.0010.050.013
5 to 90.0010.050.013
10 to 140.0010.050.013
15 to 190.0020.050.013
20 to 240.0050.050.013
25 to 290.010.050.013
30 to 340.0160.050.013
35 to 390.0230.0530.013
40 to 440.0290.060.015
45 to 490.0390.0750.019
50 to 540.0580.1040.027
55 to 590.0720.1490.042
60 to 640.1020.2240.069
65 to 690.1170.3070.105
70 to 740.1460.3860.149
75 to 790.1770.4610.203
80+0.180.7090.58
SourceVerity et al. 2020 corrected for non-uniform attack rate in China (see MRC GIDA Report 12) Adjusted from IFR distributional shape in Verity et al. 2020 to give an overall proportion of cases requiring critical care of ~30% to match UK data Calculated from IFR in Verity et al. 2020 corrected for non-uniform attack rate in China (see MRC GIDA Report 12) given the 50% fatality rate in critical care.

HIC – high-income country; IFR – infection fatality ratio; LIC – low-income country; LMIC – lower middle-income country.

Country-Specific Inputs

Population sizes and age distributions by country are from the 2020 World Population Prospects published by the United Nations.

Contact matrices are obtained from a systematic review of social contact surveys including those available through the socialmixR package. These were adjusted to give symmetric age-specific contact rates for each country.

Data on the number of general hospital beds per 1,000 population are obtained from the World Bank. However, many of these were not recent (earlier than 2015). A boosted-regression tree-based modelling approach was used to obtain contemporary estimates using the following covariates: maternal mortality (per 100,000 live births), access to electricity (% of population), population aged 0-14 years (% of population), pupil-teacher ratio in secondary school, rural population (% of population), domestic government health expenditure (% of GDP), infant mortality (per 1,000 live births), the proportion of children enrolled in secondary school, geographical region and income group (with the latter two covariates categorised according to the World Bank’s definitions).

Data on critical care capacity were derived from three sources: two previous reviews in low-income countries and Asia respectively, and our own systematic review (MRC GIDA Report 12). This generated 57 data points across all four World Bank income strata. As above, boosted regression tree models were used to obtain estimates for each country using the same set of covariates.

For both bed types, our estimates are multiplied by the population to give indicative values in the interface of total number of hospital beds and total number of critical care beds for each country. These values do not represent available beds. Both numbers can be changed by the user to incorporate local data on either total bed numbers or available beds.

Model Calibration

The stochastic squire model (https://github.com/mrc-ide/squire) is fitted to the reported daily deaths in each country by allowing two parameters to vary: the start date of the epidemic and the initial R0 in the absence of intervention. The parameter space is explored using a grid search with the start date constrained to occur before the first death due to COVID-19. We use a particle filter to explore the likelihood for a given parameter pair (R0 and start date). For a given parameter pair, 100 simulations are conducted. For each day recorded in the data, the likelihood of each simulation is calculated by comparing the daily deaths estimated to the reported deaths in the European Centres for Disease Control data, assuming the number of deaths is described by a negative binomial distribution with a spread equal to 2 to account for overdispersion. Simulations are then “filtered” by systematically resampling from the trajectories based on their log likelihood. The overall likelihood for a parameter pair is given by the sum of the mean likelihoods at each time step, which is used to identify the best fitting R0 and start date pair.

Key References

Walker P, Whittaker C, Watson O et al. (2020). The global impact of COVID-19 and strategies for mitigation and suppression. https://doi.org/10.25561/77735

Implementation

Both the stochastic and deterministic models here were developed using odin, a framework developed by the reside group in the MRC Centre for Global Infectious Disease Analysis, and compiled to JavaScript using odin.js. All models developed are available in the R package squire. Automation of model fitting was conducted using orderly.