We suppose the vaccination to be a proportion of immune individuals in the population, who are resistant to disease. For simplicity, in all our BRW models, we assume that the vaccination process does not depend on time, what allows to investigate spatial properties of viral evolution.'
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**[Branching Random Walks and their Applications for Epidemic Modelling]{}**

*[Elizaveta Ermakova, Polina Makhmutova, Elena Yarovaya]{}*

Introduction
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Branching processes are widely used in investigating the viral epidemic evolution [@GMS-B:10; @BGMS-B:10; @FF:14; @W:14]. In the work, we suggest to apply for viral epidemic modelling an important class of stochastic processes, the branching processes with the transport of particles which is commonly called the branching walks or branching random walks (BRWs). This allows us to investigate not only behavior of the particle population, but also its spatial distribution. For this, we consider a few models of continuous-time BRWs on the multidimensional lattice $\mathbb{Z}^d$, $d\ge 1$. In these models, the transport of particles (infected individuals or virus particles) is described by a symmetric random walk on $\mathbb{Z}^d$, see, e.g., [@YarBRW:r]. Processes of birth and death of particles are represented by a continuous-time Bienayme-Galton-Watson processes at the lattice points, called branching sources, see, e.g., [@YarBRW:r]. A special 