Predicting the course of Covid-19 and other epidemic and endemic disease

Abstract

AbstractThe Gompertz Function is an accurate model for epidemics from Cholera in 1853 to Spanish Flu in 1918 and Ebola in 2014. It also describes the acute phase of annual outbreaks of endemic influenza and in all of these instances it has significant predictive power.For Covid-19, we show that the Gompertz Function provides accurate forecasts not just for cases and deaths but, independently, for hospitalisations, intensive care admissions and other medical requirements. In particular Gompertz Function projections of healthcare requirements have been reliable enough to allow planning for: hospital admissions,intensive care admissions,ventilator usage, peak loads and duration.Analysis of data from the ‘Spanish Flu’ pandemic and the endemic influenza cycle reveals alternating periods of Gompertz Function growth and linear growth in cumulative cases or deaths. Linear growth means the Reproduction Number is equal to 1 which in turn indicates endemicity.The same pattern has been observed with Covid-19. All the initial outbreaks ended in linear growth. Each new outbreak has been preceded by a period of linear growth and has ended with a transition from Gompertz Function growth to linear growth. This suggests that each of these outbreak cycles ended with a transition to endemicity for the current dominant strain and that the normal seasonal respiratory virus periods will continue to see new outbreaks. It remains to be seen if widespread vaccination will disrupt this cyclicality.Because both Gompertz Function Growth and linear growth are accurately predictable, the forecasting problem is reduced to identifying the transition between these modes and to improving the performance in the early Gompertz Function growth phase where its predictive power is lowest.The dynamics of the Gompertz Function are determined by the Gumbel probability distribution. This is an exceptional distribution with respect to the geometry determined by the affine group on the line which is the key to the role of the Gumbel distribution as an Extreme Value Theory attractor. We show that this, together with the empirically observed asymmetry in epidemic data, makes the Gompertz Function growth essentially inevitable in epidemic models which agree with observations.