Séminaire des Doctorants et Doctorantes

# Invasion of cooperative parasites in moderately structured host populations

## by Mr Vianney Brouard (UMPA)

Europe/Paris
Fokko Ducloux (ICJ)

### Fokko Ducloux

#### ICJ

Description

Certain defence mechanisms of phages (viruses infecting bacteria) against the immune system of their bacterial host rely on cooperation. Motivated by this example, we will present in this talk a model dealing with the invasion probabilities of cooperative parasites in moderately structured host populations.

More precisely, in the model we will assume that hosts occupy the $N$ vertices of a configuration model and that offspring parasites move to neighbouring vertices to infect new hosts in discrete generations. Parasites will (usually) reproduce only when infecting a host simultaneously and then generate many offspring. In this regime, we will identify and analyse the spatial scale of the population structure (comparison between parameter of the configuration model and the offspring number of parasites) at which invasion of parasites achieve a phase transition by turning from being an unlikely to an highly probable event.

The study of the model will be guided first by the analysis of epidemics on random graphs, and especially by using couplings (from above and below) with (truncated) Galton-Watson processes (having "close" offspring distribution) until $N^{\alpha}$ hosts get infected for some $\alpha$ sufficiently large. And then, we will show that after exceeding the level $N^{\alpha}$ of infected hosts, with high probability the epidemic process accelerates so much that in a finite number of generations the remaining hosts get infected.