Pandemic infection rates are deterministic but cannot be modeled

Abstract

The covid-19 infection rates for a large number of infections collected from a large number of different sites are well defined with a negligible scatter. The simplest invertible iterated map, exponential growth and decay, emerges from country-wide histograms whenever Tchebychev's inequality is satisfied to within several decimal places. This is one point. Another is that failed covid-19 pandemic model predictions have been reported repeatedly by the news media. Model predictions fail because the observed infection rates are beyond modeling: any model that uses fixed rates or uses memory or averages of past rates cannot reproduce the data on active infections. When those possibilities are ruled out, then little is left. Under lockdown and social distancing, the rates unfold daily in small but unforeseeable steps, they are algorithmically complex. We can, however, use two days in the daily data, today and any single day in the past (generally yesterday), to make a useful forecast of future infections. No model provides results better than this simple forecast. We analyze the actual doubling times for covid-19 data and compare them with our predicted doubling times. Flattening and peaking are precisely defined. We identify and study the separate effects of social distancing vs recoveries in the daily infection rates. Social distancing can only cause flattening but recoveries are required in order for the active infections to peak and decay. Three models and their predictions are analyzed. Pandemic data for Austria, Germany, Italy, the USA, the UK, Finland, China, Taiwan, and Sweden are discussed.