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

Abstract: More and more countries show 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: exponential 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 number of infections and the expected final date. Two different extrapolation methods (logistic and parabolic) were used. Both methods agree on the order of magnitude of saturation and end dates. Global infections rates are analyzed with the same methods. The relevance and accuracy of these extrapolations is discussed.