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

Abstract

Rapid evidence-based decision-making and public policy based on quantitative modelling and forecasting by local and regional National Health Service (NHS-UK) managers and planners in response to the deadly severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2), a virus causing COVID-19, has largely been missing. In this pilot study, we present a data-driven epidemiological modelling framework that allows to integrate quantitative modelling, validation and forecasting based on current available local and regional datasets to investigate and mitigate the impact of COVID-19 on local NHS hospitals in terms of healthcare demand and capacity as well as allowing for a systematic evaluation of the predictive accuracy of the modelling framework for long-term forecasting. We present an epidemiological model tailored and designed to meet the needs of the local health authorities, formulated to be fitted naturally to datasets which incorporate regional and local demographics. The model yields quantitative information on the healthcare demand and capacity required to manage and mitigate the COVID pandemic at the regional level. Furthermore, the model is rigorously validated using partial historical datasets, which is then used to demonstrate the forecasting power of the model and also to quantify the risk associated with the decision taken by healthcare managers and planners. Model parameters are fully justified, these are derived purely based on the time series data available at the regional level, with minimal assumptions. Using these inferred parameters, the model is able to make predictions under which secondary waves and re-infection scenarios could occur. Hence, our modelling approach addresses one of the major criticisms associated with the lack of transparency and precision of current COVID-19 models. Our approach offers a robust quantitative modelling framework where the probability of the model giving a wrong or correct prediction can be quantified.

Reformulating the SIR model in terms of the number of COVID-19 detected cases: well-posedness of the observational model

“…As described in [15], since the data is described by the infectious compartment I, we need to re-write the equations ( 1) and (2) purely in terms of I. We note that due to the conservation of population property, we in fact do not need to consider (3) as R(t) = N − (S(t) + I(t)).…”

“…This observational model gives us an intuitive understanding of what parameters can be identified and how the data affects different compartments in the model. A standard procedure is to treat the mathematical model as an initial value problem and to either fit or seed when the initial infection might have been [8,9,11,15,24,25]. What we argue in this paper is that, using the data available, one can in fact treat the problem as a boundary value problem and that the formulation of the observational model as a boundary value problem is well-posed.…”

“…Since then, lots of other models answering questions about COVID-19 have been created pushing the frontier of the field, such as [10,11,12,13,14]. However models of grandeur like the Imperial College Model are difficult to validate due to the number of assumptions, the nature of the assumptions, and the lack of data available to cross-reference against the model outputs [15,16,17,18,19]. This opens up two questions: the question of modelling approaches and the question of data availability and parameter identification.…”

“…On the other hand, using a simpler model may allow for validation against data but has little forecasting power. Taking a data-driven approach to the derivation of a model, using a principle like Occam's razor, is becoming popular amongst the community, but requires good quality data [12,15,16,18,19,20,21]. The global movement for setting up dashboards and repositories where COVID-19 data is publicly accessible has dramatically improved the ability to progress mathematical modelling, such as in [22,23].…”

“…In particular, there is often not a one-to-one correspondence between data and direct parameter or compartment in a model, especially when considering daily snapshots of an epidemic for example. This is the main motivation behind the so-called "observational model", a representation of an SIR type model described only in terms of the model parameters and compartments that are captured by the mathematical interpretation of the data [15]. This observational model gives us an intuitive understanding of what parameters can be identified and how the data affects different compartments in the model.…”