The Sussex COVID-19 Modelling Cell: the methods and successes of a collaboration between public health teams in local authorities, NHS hospital trusts, NHS commissioners, and universities.

BACKGROUND: The Sussex Modelling Cell (SMC) is a consortium, formed during the COVID-19 pandemic, of representatives from NHS Sussex, and the local authorities and universities in Sussex. The SMC aimed to provide public health teams with local-data-driven modelling, data analysis, and policy and commissioning advice to mitigate the impact of the pandemic on the local population. It also aimed to answer operational questions, since the Government's forecasts were not suitably applicable. METHODS: From March 23, 2020, the SMC met (virtually) every Thursday to monitor COVID-19 situation reports, answer queries related to data and modelling, and provide interpretations of data or reports from many internal and external sources. SMC also provided quantitative information for public health teams to use within their organisations to advise on the local epidemic picture. Among other tools, the SMC calibrated a mathematical model to local COVID-19 data that could forecast health-care and hospital demand and COVID-19-related deaths. FINDINGS: Throughout the pandemic, the SMC provided scientific and data-driven evidence on the necessity of body storage contracts, monetary support for urgent care, and operational adjustments surrounding health-care provisions. The scientific evidence was generated and used repeatedly in each organisation to make beneficial decisions in a time of crisis. Although chasing an ever-changing pandemic picture was challenging, our swift reaction to national policy and pandemic changes allowed us to support policymakers, reduce anxiety, and provide clarity on the next steps. Our collaboration is one among few across the country and thus should be not only celebrated but also replicated, with appropriate resources and funding. INTERPRETATION: Besides mitigating the direct impact of the COVID-19 situation in Sussex, we have established a scientific collaboration relationship, in contrast to a customer-consultant setting, allowing the group to incorporate both the technical and applied perspectives into the work. With a clear structure, ethos and methodology, the SMC is able to step into the gap between academia and public health modelling to consider different impactful questions of operational importance where underlying complicated models exist, such as waiting times or system demand and capacity, and provide data analytic upskilling to public health teams. FUNDING: Brighton and Hove City Council, East and West Sussex County Council, and Sussex Health and Care Partnership.

A hospital demand and capacity intervention approach for COVID-19.

The mathematical interpretation of interventions for the mitigation of epidemics in the literature often involves finding the optimal time to initiate an intervention and/or the use of the number of infections to manage impact. Whilst these methods may work in theory, in order to implement effectively they may require information which is not likely to be available in the midst of an epidemic, or they may require impeccable data about infection levels in the community. In reality, testing and cases data can only be as good as the policy of implementation and the compliance of the individuals, which implies that accurately estimating the levels of infections becomes difficult or complicated from the data that is provided. In this paper, we demonstrate a different approach to the mathematical modelling of interventions, not based on optimality or cases, but based on demand and capacity of hospitals who have to deal with the epidemic on a day to day basis. In particular, we use data-driven modelling to calibrate a susceptible-exposed-infectious-recovered-died type model to infer parameters that depict the dynamics of the epidemic in several regions of the UK. We use the calibrated parameters for forecasting scenarios and understand, given a maximum capacity of hospital healthcare services, how the timing of interventions, severity of interventions, and conditions for the releasing of interventions affect the overall epidemic-picture. We provide an optimisation method to capture when, in terms of healthcare demand, an intervention should be put into place given a maximum capacity on the service. By using an equivalent agent-based approach, we demonstrate uncertainty quantification on the likelihood that capacity is not breached, by how much if it does, and the limit on demand that almost guarantees capacity is not breached.

Reformulating the susceptible-infectious-removed model in terms of the number of detected cases: well-posedness of the observational model.

Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data are typically akin to a boundary value-type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this paper, we reformulate the classical susceptible-infectious-recovered system in terms of the number of detected positive infected cases at different times to yield what we term the observational model. We then prove the existence and uniqueness of a solution to the boundary value problem associated with the observational model and present a numerical algorithm to approximate the solution. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Predicting and forecasting the impact of local outbreaks of COVID-19: use of SEIR-D quantitative epidemiological modelling for healthcare demand and capacity.

BACKGROUND: The world is experiencing local/regional hotspots and spikes in the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which causes COVID-19 disease. We aimed to formulate an applicable epidemiological model to accurately predict and forecast the impact of local outbreaks of COVID-19 to guide the local healthcare demand and capacity, policy-making and public health decisions. METHODS: The model utilized the aggregated daily COVID-19 situation reports (including counts of daily admissions, discharges and bed occupancy) from the local National Health Service (NHS) hospitals and COVID-19-related weekly deaths in hospitals and other settings in Sussex (population 1.7 million), Southeast England. These data sets corresponded to the first wave of COVID-19 infections from 24 March to 15 June 2020. A novel epidemiological predictive and forecasting model was then derived based on the local/regional surveillance data. Through a rigorous inverse parameter inference approach, the model parameters were estimated by fitting the model to the data in an optimal sense and then subsequent validation. RESULTS: The inferred parameters were physically reasonable and matched up to the widely used parameter values derived from the national data sets by Biggerstaff M, Cowling BJ, Cucunubá ZM et al. (Early insights from statistical and mathematical modeling of key epidemiologic parameters of COVID-19, Emerging infectious diseases. 2020;26(11)). We validate the predictive power of our model by using a subset of the available data and comparing the model predictions for the next 10, 20 and 30 days. The model exhibits a high accuracy in the prediction, even when using only as few as 20 data points for the fitting. CONCLUSIONS: We have demonstrated that by using local/regional data, our predictive and forecasting model can be utilized to guide the local healthcare demand and capacity, policy-making and public health decisions to mitigate the impact of COVID-19 on the local population. Understanding how future COVID-19 spikes/waves could possibly affect the regional populations empowers us to ensure the timely commissioning and organization of services. The flexibility of timings in the model, in combination with other early-warning systems, produces a time frame for these services to prepare and isolate capacity for likely and potential demand within regional hospitals. The model also allows local authorities to plan potential mortuary capacity and understand the burden on crematoria and burial services. The model algorithms have been integrated into a web-based multi-institutional toolkit, which can be used by NHS hospitals, local authorities and public health departments in other regions of the UK and elsewhere. The parameters, which are locally informed, form the basis of predicting and forecasting exercises accounting for different scenarios and impacts of COVID-19 transmission.