The number of infections and the number of fatalities in the 2019 novel coronavirus epidemics follows a remarkably regular trend. Since the end of January , the ratio of fatalities per infection is about 2\% and remarkably stable. The increase appears to be roughly exponential , but with an e-folding time that gradually increases from just two days at the end of January to about ten days by February 9. Here we show that, since January 20 , the number of fatalities and infections increases quadratically and not exponentially, as widely believed. At present, no departure from this behavior can be seen, allowing tentative predictions to be made for the next 1-2 months. Contrary to the usual exponential growth, a quadratic growth is the result of control interventions. It can be explained by spreading on the periphery of a bulk structure, which can be geometrical or sociological nature .
The temporal growth in the number of deaths in the COVID-19 epidemic is subexponential. Here we show that a piecewise quadratic law provides an excellent fit during the thirty days after the first three fatalities on January 20 and later since the end of March 2020. There is also a brief intermediate period of exponential growth. During the second quadratic growth phase, the characteristic time of the growth is about eight times shorter than in the beginning, which can be understood as the occurrence of separate hotspots. Quadratic behavior can be motivated by peripheral growth when further spreading occurs only on the outskirts of an infected region. We also study numerical solutions of a simple epidemic model, where the spatial extend of the system is taken into account. To model the delayed onset outside China together with the early one in China within a single model with minimal assumptions, we adopt an initial condition of several hotspots, of which one reaches saturation much earlier than the others. At each site, quadratic growth commences when the local number of infections has reached a certain saturation level. The total number of deaths does then indeed follow a piecewise quadratic behavior .
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number of infections and
temporal growth in
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fatalities in the 2019 novel coronavirus epidemics follows a remarkably regular trend. Since the end of January , the ratio of fatalities per infection is about 2\% and remarkably stable. The increase appears to be roughly exponential , but with an e-folding time that gradually increases from just two days at the end of January to about ten days by February 9. Here we show that, since January
deaths in the COVID-19 epidemic is subexponential. Here we show that a piecewise quadratic law provides an excellent fit during the thirty days after the first three fatalities on January
R
, the number of fatalities and infections increases quadratically and not exponentially, as widely believed. At present, no departure from this
and later since the end of March 2020. There is also a brief intermediate period of exponential growth. During the second quadratic growth phase, the characteristic time of the growth is about eight times shorter than in the beginning, which can be understood as the occurrence of separate hotspots. Quadratic
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seen, allowing tentative predictions to be made for the next 1-2 months. Contrary to the usual exponential growth, a quadratic growth is the result of control interventions. It can be explained by spreading on the periphery of a bulk structure, which can be geometrical or sociological nature
motivated by peripheral growth when further spreading occurs only on the outskirts of an infected region. We also study numerical solutions of a simple epidemic model, where the spatial extend of the system is taken into account. To model the delayed onset outside China together with the early one in China within a single model with minimal assumptions, we adopt an initial condition of several hotspots, of which one reaches saturation much earlier than the others. At each site, quadratic growth commences when the local number of infections has reached a certain saturation level. The total number of deaths does then indeed follow a piecewise quadratic behavior