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We consider a continuous-time branching random walk on a multidimensionallattice with two types of particles and an infinite number of initialparticles. The main results are devoted to the study of the generating functionand the limiting behavior of the moments of subpopulations generated by asingle particle of each type. We assume that particle types differ from eachother 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 eachlattice point and recurrent random walk of particles, the effect of limitspatial clustering of particles over the lattice is studied. A modelillustrating epidemic propagation is also considered. In this model, weconsider two types of particles: infected and immunity generated. Initially,there is an infected particle that can infect others. Here, for the localnumber of particles of each type at a lattice point, we study the moments andtheir limiting behavior. Additionally, the effect of intermittency of theinfected particles is studied for a supercritical branching process at eachlattice point. Simulations are presented to demonstrate the effect of limitclustering for the epidemiological model.

Branching Random Walks with Two Types of Particles on Multidimensional Lattices