Modelling the COVID-19 Fatality Rate in England and its Regions

A model to account for the fatality rate in England and its regions is proposed. It follows the clear observation that, rather than two connected waves, there have been many waves of infections and fatalities in the regions of England of various magnitudes, usually overlapping. The waves are self-limiting, in that clear peaks are seen, particularly in reported positive test rates. The present model considers fatalities as the data reported are more reliable than positive test rates, particularly so during the first wave when so little testing was done. The model considers the observed waves are essentially similar in form and can be modelled using a single wave form, whose final state is only dependent on its peak height and start date. The basic wave form was modelled using the observed fatality rates for London, which unlike the other regions, exhibited almost completely as a single wave in the "first wave". Its form matches rather well with the "Do Nothing" model reported by Imperial College on 16th March 2020, but reduced substantially from its expected peak. There are, essentially, only two adjustable parameters used in the model, the start date of the relevant wave and its height. The modelled fatalities for each wave are summated per day and a cumulative curve is matched to that reported. The minimal number of adjustable parameters, alongside the fact that the waves invariably overlap, provides highly stringent conditions on the fitting process. Results are presented for each region for both the "first" and "second waves. High levels of accuracy are obtained with R2 values approaching 100% against the ideal fit for both waves. It can also be seen that there are fundamental differences between the underlying behaviour of the "first" and "second" waves and reasons as to why those differences have arisen is briefly discussed.