Critical fluctuations in epidemic models explain COVID‑19 post‑lockdown dynamics
Abstract
As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and
very influential to understand the epidemiological dynamics of disease spreading. The momentary
reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of
the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control
measures over time. Here we investigate critical fluctuations around the epidemiological threshold,
resembling new waves, even when the community disease transmission rate β is not signifcantly
changing. Without loss of generality, we use simple models that can be treated analytically and
results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that,
rather than the supercritical regime (infectivity larger than a critical value, β>βc) leading to new
exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, β<βc)
with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown
lifting, with r(t) ≈ 1 hovering around its threshold value.