Finite-time scaling for epidemic processes with power-law superspreading events

Area of Science:

• Epidemiology
• Mathematical Biology
• Statistical Physics

Background:

• Epidemics spread via infected individuals transmitting to secondary cases.
• Superspreading events, particularly in COVID-19, are linked to power-law distributions of secondary cases, implying infinite variance.
• Understanding outbreak dynamics is crucial for public health interventions.

Purpose of the Study:

• To investigate the outbreak survival probability in epidemics with power-law-distributed superspreading.
• To analyze the emergence of phase transitions (subcritical to supercritical) in outbreak dynamics.
• To quantify the risks associated with superspreading events.

Main Methods:

• Utilized a continuous-time branching process model.
• Analyzed the survival probability as a function of time and the basic reproductive number.
• Introduced and applied the concept of finite-time scaling, analogous to finite-size scaling.

Main Results:

• Demonstrated that power-law-tailed superspreading leads to a finite-time scaling law for outbreak survival.
• Showcased universal-like characteristics dependent only on the power-law exponent.
• Observed a constant expected number of infected individuals in the subcritical phase and superlinear growth in the critical phase (excluding extinct outbreaks).

Conclusions:

• The study clarifies the phase transition from subcritical to supercritical outbreak phases in the infinite-time limit.
• Finite-time scaling provides a framework for understanding epidemic dynamics with superspreading.
• Quantified the counterintuitive hazards, highlighting increased risk during critical epidemic phases.