Scaling law of COVID-19 cases and city size and its evolution over time

Abstract

<p>Urban scaling law quantifies the disproportional growth of urban indicators with urban population size, which is one of the simple rules behind the complex urban system. Infectious diseases are closely related to social interactions that intensify in large cities, resulting in a faster speed of transmission in large cities. However, how this scaling relationship varies in an evolving pandemic is rarely investigated and remains unclear. Here, taking the COVID- 19 epidemic in the United States as an example, we collected daily added cases and deaths from January 2020 to June 2022 in more than three thousand counties to explore the scaling law of COVID- 19 cases and city size and its evolution over time. Results show that COVID- 19 cases super- linearly scaled with population size, which means cases increased faster than population size from a small city to a large city, resulting in a higher morbidity rate of COVID- 19 in large cities. Temporally, the scaling exponent that reflects the scaling relationship stabilized at around 1.25 after a fast increase from less than one. The scaling exponent gradually decreased until it was close to one. In comparison, deaths caused by the epidemic did not show a super-linear scaling relationship with population size, which revealed that the fatality rate of COVID-19 in large cities was not higher than that in small or medium-sized cities. The scaling exponent of COVID- 19 deaths shared a similar trend with that of COVID- 19 cases but with a lag in time. We further estimated scaling exponents in each wave of the epidemic, respectively, which experienced the common evolution process of first rising, then stabilizing, and then decreasing. We also analyzed the evolution of scaling exponents over time from regional and provincial perspectives. The northeast, where New York State is located, had the highest scaling exponent, and the scaling exponent of COVID- 19 deaths was higher than that of COVID-19 cases, which indicates that large cities in this region were more prominently affected by the epidemic. This study reveals the size effect of infectious diseases based on the urban scaling law, and the evolution process of scaling exponents over time also promotes the understanding of the urban scaling law. The mechanism behind temporal variations of scaling exponents is worthy of further exploration.</p>