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During the COVID pandemic, periods of exponential growth of the disease havebeen mitigated by containment measures that in different occasions haveresulted in a power-law growth of the number of cases. The first observation ofsuch behaviour has been obtained from 2020 late spring data coming from Chinaby Ziff and Ziff in Ref. [1]. After this important observation the power-lawscaling (albeit with different exponents) has also been observed in othercountries during periods of containment of the spread. Early interpretations ofthese results suggest that this phenomenon might be due to spatial effects ofthe spread. Here we show that temporal modulations of infectivity ofindividuals due to containment measures can also cause power-law growth of thenumber of cases over time. To this end we propose a stochastic well-mixedSusceptible-Infected-Removed (SIR) model of epidemic spreading in presence ofcontainment measures resulting in time-dependent infectivity and we explore thestatistical properties of the resulting branching process at criticality. Weshow that at criticality it is possible to observe power-law growth of thenumber of cases with exponents ranging between one and two. Our asymptoticanalytical results are confirmed by extensive Monte Carlo simulations. Althoughthese results do not exclude that spatial effects might be important inmodulating the power-law growth of the number of cases at criticality, thiswork shows that even well-mixed populations may already feature non-trivialpower-law exponents at criticality.

Critical time-dependent branching process modelling epidemic spreading with containment measures