## An epidemic model in inhomogeneous environment

We introduce an epidemic model on the complete graph $\mathbb K_n$ on $n$ vertices in a non-homogeneous setting, where the vertices may have distinct types. Different types differ in the probability of getting infected, and/or in the capacity of infecting other vertices. This generalizes the model in a paper of Comets et al, 2014. We prove laws of large numbers and central limit theorems for the the total duration of the process and for the number of infected vertices, respectively, when $n\to\infty$. By coupling the epidemic model with a Poisson process, we also obtain continuous-time counterparts of the above-mentioned limit results. Moreover, we also prove that when all individuals have the same spread capacity, then a population with inhomogeneous susceptibility is less affected by the epidemics than a homogeneous population.

Area: CS10 - Random walks and branching processes (Fabio Zucca)

Keywords: branching process, multitype Galton-Watson process, coupon collector

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