# 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.