B1668
Title: Continuous time multitype branching random walks
Authors: Elena Yarovaya - Lomonosov Moscow State University (Russia) [presenting]
Abstract: Continuous-time multitype branching random walks are considered on a multidimensional lattice. The main results are devoted to the study of the generating function and the limiting behaviour of the moments of subpopulations generated by a single particle of each type. It is assumed that particle types differ from each other not only by the laws of branching, as in multi-type branching processes, but also by the laws of walking. For a critical branching process at each lattice point and recurrent random walk of particles, the effect of limited spatial clustering of particles over the lattice is studied. A model illustrating epidemic propagation is also considered. Two types of particles are considered: infected and immunity generated. Initially, there is an infected particle that can infect others. For the local number of particles of each type at a lattice point, the moments and their limiting behaviour are studied. Additionally, the effect of intermittency of the infected particles is studied for a supercritical branching process at each lattice point. Simulations are presented to demonstrate the effect of limit clustering for the epidemiological model.
