Branching Random Walks with Two Types of Particles on Multidimensional Lattices

We consider a continuous-time branching random walk on multidimensional lattice with two types of particles and an infinite number initial particles. The main results are devoted to the study generating function limiting behavior moments subpopulations generated by single particle each type. assume that differ from other not only laws branching, as in multi-type processes, but also walking. For critical process at point recurrent particles, effect limit spatial clustering over is studied. A model illustrating epidemic propagation considered. In this model, we particles: infected immunity generated. Initially, there can infect others. Here, for local type point, their behavior. Additionally, intermittency studied supercritical point. Simulations presented demonstrate epidemiological model.