Physics-informed machine learning for the COVID-19 pandemic: Adherence to social distancing and short-term predictions for eight countries

The spread of COVID-19 during the initial phase of the first half of 2020 was curtailed to a larger or lesser extent through measures of social distancing imposed by most countries. In this work, we link directly, through machine learning techniques, infection data at a country level to a single number that signifies social distancing effectiveness. We assume that the standard SIR model gives a reasonable description of the dynamics of spreading, and thus the social distancing aspect can be modeled through time-dependent infection rates that are imposed externally. We use an exponential ansatz to analyze the SIR model, find an exact solution for the time-independent infection rate, and derive a simple first-order differential equation for the time-dependent infection rate as a function of the infected population. Using infected number data from the "first wave" of the infection from eight countries, and through physics-informed machine learning, we extract the degree of linear dependence in social distancing that led to the specific infections. We find that in the two extremes are Greece, with the highest decay slope on one side, and the US on the other with a practically flat "decay". The hierarchy of slopes is compatible with the effectiveness of the pandemic containment in each country. Finally, we train our network with data after the end of the analyzed period, and we make week-long predictions for the current phase of the infection that appear to be very close to the actual infection values.