Bastian Prasse: Epidemics on networks: from complicated structures to simple dynamics

Time: Wed 2021-12-08 15.15 - 16.00

Location: Kräftriket, House 6, Room 306

Lecturer: Bastian Prasse (ECDC, Solna)

Abstract

The spread of an infectious disease crucially depends on the contact patterns of individuals, which range from superspreaders and clustered communities to isolated individuals with only a few regular contacts. The contact network specifies all contacts either between individuals in a population or, on a coarser scale, the contacts between groups of individuals, such as households, age groups or geographical regions. The structure of the contact network has a decisive impact on the viral dynamics. However, in most scenarios, the precise network structure is unknown, which constitutes a tremendous obstacle to understanding and predicting epidemic outbreaks.

This talk focusses on a stark contrast: network structures are complicated, but viral dynamics on networks are simple. Specifically, denote the $$N \times 1$$ viral state vector by $$I(t) = (I_1(t), \dots, I_N(t))$$, where N is the network size and $$I_i(t)$$ is the infection probability of individual i at time t. The dynamics are “simple” in the way that the state $$I(t)$$ evolves in a subspace X of $$\mathbb{R}^N$$ of astonishingly low dimension $$\dim(X) \ll N$$. The low dimensionality of the viral dynamics has far-reaching consequences. First, it is possible to predict an epidemic outbreak, even without knowing the network structure. Second, provided that the basic reproduction number $$R_0$$ is close to one, the Susceptible-Infectious-Susceptible (SIS) epidemic model has a closed-form solution for arbitrarily large and heterogeneous contact networks.