Evolving urban allometric scaling law of the COVID-19 epidemic in the United Kingdom

Infectious diseases depend on intensified social intercourse within large cities, resulting in a superlinear allometric scaling law with city size. But how this scaling relationship changes throughout an evolving pandemic is seldom studied and remains unclear. Here, we investigate allometric scaling laws between cases/deaths and city size and their temporal evolution using daily COVID19 cases/deaths of cities in the United Kingdom from March 2020 to May 2022. Results indicate that cases exhibit a super-linear scaling pattern with city size, revealing higher morbidity in large cities. Temporally, scaling exponents stabilized at around 1.25 after a rapid increase from less than one and then decreased to one. Scaling exponents of COVID-19 deaths exhibited a comparable trend to cases but with a lag in time and a weaker super-linear relationship. Scaling exponents increased first, then stabilized, and then decreased during each wave. Temporal variations of scaling exponents reveal the spatial diffusion of infectious diseases from large to small cities, whose mechanism needs further exploration.