Epidemic plateau in critical SIR dynamics with non-trivial initial conditions

TL;DR

This paper demonstrates that epidemic plateaus observed during COVID-19 containment can be explained by critical SIR dynamics with non-trivial initial conditions, revealing complex outbreak behaviors and significant fluctuations.

Contribution

It extends the critical SIR model to account for large initial infected populations due to containment measures, providing theoretical and numerical insights into outbreak size and duration.

Findings

Outbreak size increases with initial infected count.

Outbreak duration varies non-monotonically with initial infected count.

Fluctuations in outbreak metrics are large near criticality.

Abstract

Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by time series of daily infections plateauing over extended periods of time. We prove that such a dynamical pattern is compatible with critical Susceptible-Infected-Removed (SIR) dynamics. In traditional analyses of the critical SIR model, the critical dynamical regime is started from a single infected node. The application of containment measures to an ongoing epidemic, however, has the effect to make the system enter in its critical regime with a number of infected individuals potentially large. We describe how such non-trivial starting conditions affect the critical behavior of the SIR model. We perform a theoretical and large-scale numerical investigation of the model. We show that the expected outbreak size is an increasing function of the initial number of infected individuals, while the expected duration of the outbreak is a non-monotonic function of the initial number of infected individuals. Also, we precisely characterize the magnitude of the fluctuations associated with the size and duration of the outbreak in critical SIR dynamics with non-trivial initial conditions. Far from heard immunity, fluctuations are much larger than average values, thus indicating that predictions of plateauing time series may be particularly challenging.