Journal
PHYSICAL REVIEW E
Volume 105, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.105.064122
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Funding
- Spanish MICINN [PGC-FIS2018-099629-B-I00]
- Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in RD [CEX2020-001084-M]
- CERCA Programme/Generalitat de Catalunya
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This study uses a continuous-time branching process to uncover the finite-time scaling law of the survival probability of outbreaks under power-law-tailed superspreading conditions, and reveals a phase transition phenomenon. The research also demonstrates the counterintuitive hazards posed by this type of superspreading.
Epidemics unfold by means of a spreading process from each infected individual to a variable number of secondary cases. It has been claimed that the so-called superspreading events of the COVID-19 pandemic are governed by a power-law-tailed distribution of secondary cases, with no finite variance. Using a continuous-time branching process, we demonstrate that for such power-law-tailed superspreading, the survival probability of an outbreak as a function of both time and the basic reproductive number fulfills a ???finite-time scaling??? law (analogous to finite-size scaling) with universal-like characteristics only dependent on the power-law exponent. This clearly shows how the phase transition separating a subcritical and a supercritical phase emerges in the infinite-time limit (analogous to the thermodynamic limit). We also quantify the counterintuitive hazards posed by this superspreading. When the expected number of infected individuals is computed removing extinct outbreaks, we find a constant value in the subcritical phase and a superlinear power-law growth in the critical phase.
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