Super Spreaders and Other Statistical Swings in Epidemic Models

by | Apr 13, 2020 | Mathematics, Research, School of Physical and Mathematical Sciences

3D rendering of the magnified Coronavirus cell or Covid-19 cell disease in blood.

Mathematical models of epidemics are crucial tools for preventing and controlling outbreaks of infectious diseases, such as the novel coronavirus currently ravaging the world. In such models, it is important to be able to describe the effects of ‘super spreaders’, infected individuals who go on to infect unusually many other people.

The 2020 novel coronavirus pandemic has seen numerous high-profile super spreader events, such as South Korea’s “patient 31”, who is believed to have passed on the disease to over 70 other members of her fringe church group.

The size of a disease outbreak in a heavy-tailed model (blue curve) and in a standard model (orange curve). In the heavy-tailed model, the disease can abruptly go extinct despite the presence of sudden shocks, wheras in the standard model the disease remains endemic.

However, large statistical fluctuations in disease outbreaks are not necessarily always bad news. Nicolas Privault and Liang Wang, two mathematical researchers at NTU’s School of Physical and Mathematical Sciences, have studied how an outbreak’s size can suddenly fluctuate downward, causing the pathogen to go extinct. Their paper was uploaded to the arxiv pre-print server in November 2019, prior to the coronavirus pandemic.

The model studied by Privault and Wang accounts for the possibility of both super spreader events and sharp drop events. Although these two types of events are polar opposites, they are both driven by the fact that the probability distributions describing disease transmission can have “heavy tails”. With such probability distributions, it is relatively likely to achieve outcomes that are very different from the average outcome.

Privault and Wang derived a rigorous proof about the requirements for disease extinction events to happen in this framework. Their work used sophisticated mathematical techniques based on “heavy tailed stochastic increments”.  They showed that the extinction of a disease depends not only on basic characteristics of the underlying probability distributions, such as the standard deviation, but also on the shapes of the distributions.

For more information, refer to the pre-print paper:

  1. Privault and L. Wang, Stochastic SIR Levy jump model with infinite activity, arxiv:1911.12924
Skip to toolbar