Predictions for Europe for the Covid-19 pandemic from a SIR model

We develop and apply a simplified SIR model to current data for the 2019-2020 SARS-Cov-2/Covid-19 pandemic for the United Kingdom (UK) and eight European countries: Norway, Sweden, Denmark, the Netherlands, France, Germany, Italy and Spain. The most important result of the model was the identification and segregation of pandemic characteristics into two distinct groups: those that are invariant across countries, and those that are highly variable. Amongst the former is the infective period T_L, which was very similar for all countries, with an average value of <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20114058v2_inline1.gif"/></alternatives></inline-formula> days. The other invariants were T_R, the average time between contacts and R = N_C, the average number of contacts while infective. We find <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20114058v2_inline2.gif"/></alternatives></inline-formula> days and <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20114058v2_inline3.gif"/></alternatives></inline-formula>. In contrast to these invariants, there was a highly variable time lag T_D between the peak in the daily number of infected individuals and the peak in the daily number of deaths, ranging from a low of T_D = 4 days for Italy and Denmark, to a high of T_D = 17 for Norway. The mortality probability among identified cases was also highly variable, ranging from low values 3.5%, 5% and 5% for Norway, Denmark and Germany respectively to high values of 18%, 18% and 20% for France, Sweden and the UK respectively. Our analysis predicts that the number of deaths per million population until the pandemic ends (defined as when the daily number of deaths is less than 5) will be lowest for Norway (45 deaths/million) and highest for the United Kingdom (628 deaths/million). Finally, we observe a small but detectable effect of average temperature on the probability α of infection in each contact, with higher temperatures associated with lower infectivity.