The COVID-19 pandemic: growth patterns, power law scaling, and saturation.

More and more countries are showing a significant slowdown in the number of new COVID-19 infections due to effective governmentally instituted lockdown and social distancing measures. We have analyzed the growth behavior of the top 25 most affected countries by means of a local slope analysis and found three distinct patterns that individual countries follow depending on the strictness of the lockdown protocols: rise and fall, power law, or logistic. For countries showing power law growth we have determined the scaling exponents. For countries that showed a strong slowdown in the rate of infections we have extrapolated the expected saturation of the total number of infections and the expected final date. Three different extrapolation methods (logistic, parabolic, and cutoff power law) were used. All methods agree on the order of magnitude of saturation and end dates. Global infection rates are analyzed with the same methods. The relevance and accuracy of these extrapolations is discussed.