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. For countries not included in the European Centres for Disease Control, we source deaths from worldometers.
The impact of interventions that have been put in place is captured using mobility data made publically available from Google, which provides data on movement in each country and highlights the percent change in visits to places of interest. We currently estimate the impact of changes in mobility on transmission as part of our model fitting. For countries without mobility data, we infer the level of mobility based on reports of government interventions (school closures, curfews, public events banned, lockdowns etc) sourced from the acaps COVID-19 government measures dataset.
The epidemic up to today’s date for each country is fixed and cannot be changed by the user. The reproductive number, Rt, calculated from this is plotted over time. The user can change Rt from today’s date going forward to reflect changes in interventions implemented for that country. As sets of interventions may be switched on and off in response to changes in a country’s epidemic growth rate, the Rt will also change. Therefore the user can define multiple phases for the epidemic, changing the estimate for Rt for different calendar periods, to explore levels transmission and healthcare demand.
The user changes the value for Rt, which represents the reproductive number i.e. the average number of COVID-19 transmissions that result from one infected individual, in a population totally susceptible to SARS-CoV-2 infection. However, as the pandemic has progressed, an increasing proportion of the population has developed immunity as a result of previous infection, which reduces the reproductive number because there are fewer individuals susceptible to infection. Therefore while the user changes Rt, covidsim.org additionally tracks Reff, the effective reproductive number, which takes into account the proportion of the population immune to infection. The user can visualise the Reff curve in addition to Rt. While the user-defined Rt value will remain constant for each phase, the Reff value will decline over that duration as more people in the population have acquired infection and subsequent immunity.
It is very hard to know how much Rt will change in response to new interventions being put in place, or by how much it may increase when interventions are relaxed. However, in countries that implemented strict lockdowns and suppressive measures, it seems unlikely that Rt will fall below the minimum Rt they achieved during first lockdown, until a vaccine becomes available. Conversely, public awareness of COVID-19 is substantially greater than at the beginning of the year, and therefore it seems unlikely that Rt will return to the maximum Rt observed at the start of the epidemic. Reasonable estimates for future Rt values should take these points into consideration. Additionally, users could gain insight on future Rt values from similar/neighbouring countries that may have already relaxed or re-implemented measures.
The Scenario Analysis 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, R0 | 3.0 days | Estimate from Europe, Flaxman et al. |
| 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 IMILD and ICASE states to capture pre-symptomatic infectivity |
| Generation Time | 6.75 days | Bi et al. 2020 |
| Mean Duration in IMild | 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 ICASE this gives a mean generation time as above |
| Mean Duration in ICase | 4.5 days | Mean 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 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 (IHospital) if die | 9 days | As above |
| Mean duration of Critical Care (IICU) 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 (IICU) if die | 11.1 days | As above |
| Mean duration of Stepdown post ICU (IRec) | 3 days | Working assumption based on unpublished UK data |
| Mean duration of hospitalisation if require critical care (ICU) but do not receive it | 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) |
| Probability of death if require critical care but do not receive it | 0.95 | Working assumption based on expert clinical opinion |
| Probability of death if require hospitalisation but do not receive it | 0.6 | Working assumption based on expert clinical opinion |
HIC – high-income country; IFR – infection fatality ratio; LIC – low-income country; LMIC – lower middle-income country; MRC GIDA – Medical Research Council Centre for Global Infectious Disease Analysis.
Age-Specific Parameters
| Age-Group | Proportion of Infections Hospitalised | Proportion of hospitalised cases requiring critical care | Proportion of hospital deaths occurring in ICU | Proportion of non-critical care cases dying | Proportion of critical care cases dying |
|---|---|---|---|---|---|
| 0 to 4 | 0.001 | 0.181 | 0.8 | 0.013 | 0.227 |
| 5 to 9 | 0.001 | 0.181 | 0.8 | 0.014 | 0.252 |
| 10 to 14 | 0.002 | 0.181 | 0.8 | 0.016 | 0.281 |
| 15 to 19 | 0.002 | 0.137 | 0.8 | 0.016 | 0.413 |
| 20 to 24 | 0.003 | 0.122 | 0.8 | 0.018 | 0.518 |
| 25 to 29 | 0.005 | 0.123 | 0.8 | 0.02 | 0.573 |
| 30 to 34 | 0.007 | 0.136 | 0.8 | 0.023 | 0.576 |
| 35 to 39 | 0.009 | 0.161 | 0.8 | 0.026 | 0.543 |
| 40 to 44 | 0.013 | 0.197 | 0.8 | 0.03 | 0.494 |
| 45 to 49 | 0.018 | 0.242 | 0.8 | 0.036 | 0.447 |
| 50 to 54 | 0.025 | 0.289 | 0.8 | 0.042 | 0.417 |
| 55 to 59 | 0.036 | 0.327 | 0.8 | 0.05 | 0.411 |
| 60 to 64 | 0.05 | 0.337 | 0.8 | 0.056 | 0.443 |
| 65 to 69 | 0.071 | 0.309 | 0.8 | 0.06 | 0.539 |
| 70 to 74 | 0.1 | 0.244 | 0.8 | 0.123 | 0.57 |
| 75 to 79 | 0.14 | 0.16 | 0.8 | 0.184 | 0.643 |
| 80+ | 0.233 | 0.057 | 0.8 | 0.341 | 0.993 |
| Source | Salje et al. | Salje et al. | Assumed | Calculated from IFR in Report 34 | Calculated from IFR in Report 34 |
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 deterministic squire model (https://github.com/mrc-ide/squire) is fitted to the reported daily deaths in each country by allowing three parameters to vary: the start date of the epidemic , the initial R0 in the absence of intervention and the effect size of changes in mobility on transmission. Where mobility data is unavailable for a country, we use government interventions to predict the mobility in a country. The parameter space is explored using a grid search with the start date constrained to occur before the first death due to COVID-19. 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. The overall likelihood for a parameter set (R0, start date and mobility effect size) is given by the sum of the likelihood at each time step, which is used to identify the best fitting R0, start date and mobility effect size.
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
Watson, O., M. Alhaffar, Z. Mehchy, C. Whittaker, et al. “Report 31: Estimating the Burden of COVID-19 in Damascus, Syria: An Analysis of Novel Data Sources to Infer Mortality under-Ascertainment.” Imperial College London, 25 Sep 2020. https://doi.org/10.25561/82443 https://www.imperial.ac.uk/media/imperial-college/medicine/mrc-gida/15-09-2020-COVID19-Report-31.pdf
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.
