Title: Multi-type branching random walks on multidimensional lattices
Authors: Yulia Makarova - Lomonosov Moscow State University (Russia) [presenting]
Daria Balashova - MSU (Russia)
Elena Yarovaya - Lomonosov Moscow State University (Russia)
Abstract: The focus is on continuous-time multi-type branching random walks (BRWs), which may be described in terms of birth, death, and walking of particles of different types on multidimensional lattices. At the initial time moment, there is at least one particle of each type at every lattice point. For BRWs with sources of branching at each lattice point the reproduction law of particles is described by a multi-type branching process, which means that every particle can produce offsprings of each type by own branching mechanism. Moreover, particles can walk over the lattice. We assume that an underlying random walk for every type of particles is symmetric, homogeneous in space and irreducible. The main objects are subpopulations of particles generated by a single particle of each type at every lattice point and all over the lattice. The differential equations for generating functions for such subpopulations and their factorial moments are obtained. Based on such results, the solutions for the first moments of particle subpopulations are studied in detail. The application of such models for describing the spread of epidemics is discussed.