Predicting the Trajectory of Any COVID19 Epidemic From the Best Straight Line
A pipeline involving data acquisition, curation, carefully chosen graphs and mathematical models, allows analysis of COVID-19 outbreaks at 3,546 locations world-wide (all countries plus smaller administrative divisions with data available). Comparison of locations with over 50 deaths shows all outbreaks have a common feature: H(t) defined as loge(X(t)/X(t-1)) decreases linearly on a log scale, where X(t) is the total number of Cases or Deaths on day, t (we use ln for loge). The downward slopes vary by about a factor of three with time constants (1/slope) of between 1 and 3 weeks; this suggests it may be possible to predict when an outbreak will end. Is it possible to go beyond this and perform early prediction of the outcome in terms of the eventual plateau number of total confirmed cases or deaths?
We test this hypothesis by showing that the trajectory of cases or deaths in any outbreak can be converted into a straight line. Specifically tY ≡ − tXN ))(/ln(ln()( , is a straight line for the correct plateau value N, which is determined by a new method, Best-Line Fitting (BLF). BLF involves a straight-line facilitation extrapolation needed for prediction; it is blindingly fast and amenable to optimization. We find that in some locations that entire trajectory can be predicted early, whereas others take longer to follow this simple functional form. Fortunately, BLF distinguishes predictions that are likely to be correct in that they show a stable plateau of total cases or death (N value). We apply BLF to locations that seem close to a stable predicted N value and then forecast the outcome at some locations that are still growing wildly. Our accompanying web-site will be updated frequently and provide all graphs and data described here.