Discussion
We have developed a deterministic ordinary differential equation model of the epidemic trajectory of COVID-19 focusing on acute and IC hospital bed capacity planning to support local NHS authorities, calibrating to SW-specific data. The model is age structured and includes time-specific implementation of current interventions (following advice and enforcement of social distancing, school closures and lockdown) to predict the potential range of COVID-19 epidemic trajectories.
Using the publicly available data on cases and deaths, combined with the early estimates of parameters from early epidemics in other settings, we predict that on 11 May 2020 a total of 5793 (95% CrI 2003 to 12 051) were infectious, which equates to 0.10% (95% CrI 0.04% to 0.22%) of the total SW population. In addition, we find that the model predicts a total of 189 048 (95% CrI 141 580 to 277 955) have had the virus but recovered, which is 3.4% (95% CrI 2.5% to 5.0%) of the SW population.
We also estimate that the total number of patients in acute hospital beds in SW on 11 May 2020 was 701 (95% CrI 169 to 1543) and in IC was 110 (95% CrI 8 to 464), while the R number has decreased from 2.6 (95% CrI 2.0 to 3.2) to 0.6 (95% CrI 0.5 to 0.7) after all interventions were enacted and fully adhered to.
The fits generally agree well with both the daily case data and the cumulative count of deaths in the SW, although the model overestimates the case data at early stages and underestimates later on (which can be seen in online supplemental figure S2A, and a scatter plot of expected vs observed outputs in online supplemental figure S2B). This could be because we are using formal fitting methods or from the under-reporting of cases in the early epidemic. When assessing model performance by projecting the numbers of cases and deaths forward from four dates in April, the model performs reasonably well, with more reliable predictions occurring when more data are used to fit the model (online supplemental figure S3A–D). Even when using around half of the available data to generate forecasts (online supplemental figure S3D), the model performs reasonably well and captures the observed data later in May, but overestimates case numbers and underestimates deaths similar to those in the main analysis and in online supplemental figure S2A. This suggests that our model could perform reasonably well at predicting COVID-19 outcomes but may still slightly overestimate case numbers and underestimate deaths.
The primary strength of this study is that we have developed generalisable and efficient modelling code incorporating disease transmission, interventions and hospital bed demand which can be adapted for use in other regional or national scenarios, with the model available on GitHub for open review and use (github.com/rdbooton/bricovmod). We have worked closely with the NHS and at CCG level to ensure the model captures key clinical features of disease management in SW hospitals and provides output data in a format relevant to support local planning. We combined local clinical expertise with detailed literature searches to ensure reasonable parameter ranges and assumptions in the presence of high levels of parameter uncertainty.
The main challenge of this work is in balancing the urgent need locally for prediction tools which are up to date (ie, not relying on the national trends to inform capacity planning) versus more exhaustive and robust methods for model comparison. The latter of which uses existing models and more time-consuming (but more robust) data-fitting methods.26 27 However, we believe that release of this paper and sharing of model code will facilitate multidisciplinary collaboration and rapid review and support future model comparison and uncertainty analyses.27
As with all models of new infections there are significant parameter uncertainties. Rapidly emerging literature is exploring a wide range of biological and epidemiological factors concerning COVID-19, but due to the worldwide nature of these studies, often parameter bands are wide and may be context specific. For example, early estimates of the basic reproduction number ranged from 1.6 to 3.8 in different locations,28 29 with an early estimate of 2.4 used in UK model projections.8 In addition, the information which informs our parameter selection is rapidly evolving as new data are made available, sometimes on a daily basis. From our initial analysis, we identified the following parameters as critical in determining the epidemic trajectory within our model—the percentage of infections which become symptomatic, the recovery time for cases which do not require hospital, the period between acute and IC occupancy, the length of stay in IC, the probability of transmission per contact and the gradual implementation of lockdown rather than immediate effect. Other parameters (such as the percentage reduction in school-age contacts from school closures) did not seem to influence the dynamic trajectory as strongly—and thus we assume point estimates for these parameters. However, for example, assuming that 95% of school-age contacts are reduced as a direct result of school closures is perhaps an overestimate, and future modelling work should address these uncertainties and their impacts on the epidemic trajectory of COVID-19 (but in this case, this value was somewhat arbitrary, and the assumption was used in the absence of school-age contact survey data). In addition, we did not explicitly model the societal effect prior to governmental advice (social distancing, school closures, lockdown), instead assuming a fixed date, before which we assume there were no interventions. This assumption may not be realistic and could have influenced the model output, but it is difficult to quantify the percentage compliance with interventions prior to the official release of governmental advice. More research is urgently needed to refine these parameter ranges and to validate these biological parameters experimentally. These estimates will improve the model as more empirical data become available. We look forward to reducing the uncertainty in these parameters so that we can make better predictions and fit the data more accurately.
We have also assumed that there is no nosocomial transmission of infection between hospitalised cases and healthcare workers, as we do not have good data for within-hospital transmission. However, front-line healthcare staff were likely to have been infected early on in the epidemic,30 which could have implications for our predicted epidemic trajectory. Our model also assumes a closed system, which may not strictly be true due to continuing essential travel. But given that up until 11 May, travel restrictions are very severe due to lockdown measures,5 any remaining inter-regional travel is likely to have minimal effects on our model outputs. In addition, we assume that the transmission dynamics of asymptomatic individuals is equal to those of symptomatic individuals due to the viral load of asymptomatic and symptomatic carriers being comparable.31 However, this assumption should be further explored in future modelling studies due to the potential for asymptomatic carriers to engage in higher risk behaviour and potentially impact the transmission dynamics of COVID-19.
Similar to most other COVID-19 models, we use a variant on a susceptible-exposed-infectious-recovered structure.8–10 16 26 32 33 We do not spatially structure the population as in other UK modelling,9 10 but we do include age-specific mixing based on POLYMOD data22 and the postlockdown CoMix study.11 We also explicitly measure the total asymptomatic infection, and the total in each of the clinically relevant hospital classes (acute or IC), which is a strength of our approach. Future models could also take into account local bed capacity within hospitals (including Nightingale centres) and accommodate the effect of demand outstripping supply leading to excess deaths, inclusive of non-hospital-based death such as is occurring within care homes. Future models should also address the way in which we have compartmentalised the flow of hospitalisation and death. From the symptomatic compartment, patients either recover or are admitted to hospital, from where they either die, recover or progress to IC. Under our assumption, the symptomatic recovery rate is equal to the hospitalisation rate, and the time taken for acute patients to move to IC is equal to the time to discharge for acute patients. These assumptions are a limitation of our model because in reality, those patients who progress to IC may have spent very little time in an acute bed (either due to rapid deterioration or presenting with severe symptoms). Future studies should assess the effects of these assumptions and consider other such progressions and outcomes for a patient with COVID-19 through the hospital. As with all modelling, we have not taken into account all possible sources of modelling mis-specification. Some of these mis-specifications will tend to increase the predicted epidemic period, and others will decrease it. One factor that could significantly change our predicted epidemic period is the underlying structure within the population leading to heterogeneity in the average number of contacts under lockdown, for example, key workers have high levels of contact but others are able to minimise contacts effectively, this might lead to an underestimate of ongoing transmission, but potentially an overestimate of the effect of releasing lockdown. We also know that there are important socioeconomic considerations in determining people’s ability to stay at home and particularly to work from home.34
Early UK modelling predicted the infection peak to be reached roughly 3 weeks from the initiation of severe lockdown measures, as taken by the UK government in mid-March.8 A more recent study factoring spatial distribution of the population indicated the peak to follow in early April due to R0 reducing to below 1 in many settings in weeks following lockdown.9 Other modelling indicated that deaths in the UK would peak in mid-late April; furthermore, that the UK would not have enough acute and IC beds to meet demand.35 While modelling from the European Centre for Disease Prevention and Control estimated peak cases to occur in most European countries in mid-April,20 these estimations were largely at a national level. Due to the expected lag of other regions behind London, these estimated peaks are likely to be shifted further into the future for the separate regions of the UK, and as shown by our model occurred in early to mid-April. This is also likely to be true for future peaks which may result from relaxing lockdowns.
Outside of the UK, a similar modelling from France32 (which went into lockdown at a similar time the UK on 17 March) predicted the peak in daily IC admissions at the end of March. Interestingly, however, when dissected by region, the peak in IC bed demand varied by roughly 2 weeks. Swiss modelling similarly predicted a peak in hospitalisation and numbers of patients needing IC beds in early April, after lockdown implementation commenced on 17 March.33 US modelling36 disaggregated by State also highlights the peak of excess bed demand varies geographically, with this peak ranging from the second week of April through to May, dependent on the State under consideration. The modelling based in France also cautioned that due to only 5.7% of the population having been infected by 11 May when the restrictions would be eased, the population would be vulnerable to a second epidemic peak thereafter.32
The ONS in England estimated that an average of 0.25% of the population had COVID-19 between 4 and 17 May 2020 (95% CI 0.16% to 0.38%),37 which is greater than the 0.10% (95% CrI 0.04% to 0.22%) we found with our model (on 11 May 2020), but with some overlap. In addition, the ONS estimated that 6.78% (95% CrI 5.21% to 8.64%) tested positive for antibodies to COVID-19 up to 24 May 2020 in England,38 and Public Health England estimated that approximately 4% (2%–6%) tested positive for antibodies to COVID-19 between 20 and 26 April 2020 in the SW.39 Compared with our model, 3.4% (95% CrI 2.5% to 5.0%) had recovered on 11 May 2020 (2 weeks later), demonstrating that our model estimates may be within sensible bounds, and further highlighting the need for more regional estimates of crucial epidemiological parameters and seroprevalence. We have assumed that individuals are not susceptible to reinfection within the model time frame; however, in future work it will be important to explore this assumption. It is not known what the long-term pattern of immunity to COVID-19 will be,40 and this will be key to understanding the future epidemiology in the absence of a vaccine or effective treatment options.
With this in mind, our findings demonstrate that there are still significant data gaps—and in the absence of such data, mathematical models can provide a valuable asset for local and regional healthcare services. This regional model will be used further in the SW as the pandemic evolves and could be used within other healthcare systems in other geographies to support localised predictions. Controlling intervention measures at a more local level could be made possible through monitoring and assessment at the regional level through a combination of clinical expertise and local policy, guided by localised predictive forecasting as presented in this study.