Colloquium Mathematics - Dr. P. Trapman

Title: Herd immunity, population structure and the second wave of an epidemic

Abstract:

Abstract: The classical herd-immunity level is defined as the fraction of a population that has to be immune to an infectious disease in order for a large outbreak of the disease to be impossible, assuming (often implicitly) that the immunized people are a uniform subset of the population.

I will discuss the impact on herd immunity if the immunity is obtained through an outbreak of an infectious disease in a heterogeneous population.

The leading example is a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemic outbreaks or waves in the same population structured by a random network. Individuals infected during the first outbreak are (partially) immune for the second one.

The first outbreak is analysed through a bond percolation model, while the second wave is approximated by a three-type branching process in which the types of individuals depend on their position in the percolation clusters used for the first outbreak. This branching process approximation enables us to calculate a threshold parameter and the probability the second outbreak is large.

This work is based on joined work with Tom Britton and Frank Ball and on ongoing work with Frank Ball, Abid Ali Lashari and David Sirl.

Reference: Britton, Ball & Trapman, (2020). A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2, To appear in Science.

https://science.sciencemag.org/content/early/2020/06/22/science.abc6810.

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