individual.

Denote by $\eta_{t}(y)$ the number of particles at the point $y\in\mathbb{Z}^d$ at time $t$. Then due to the assumption that there is just one particle at every point $x\in\mathbb{Z}^d$ at instant $t=0$ we have that the function $\eta_{t}(y)$ satisfies the following initial condition: $\eta_{0}(y)=1$ for all $y\in\mathbb{Z}^{d}$. In this model we also divide all the particles on the lattice into subpopulations, that is, we assume that each initial particle at a point $x\in \mathbb{Z}^{d}$ is a progenitor of its separate subpopulation $\eta_{x,t}$ on $\mathbb{Z}^{d}$ at time $t$. Denote by $\eta_{x, t}(y)$ the number of particles from each subpopulation at time $t$ at the point $y\in\mathbb{Z}^d$ with the initial position of the progenitor particle at the point $x$. It satisfies the initial condition $\eta_{x, 0}(y)=\delta_{x}(y)$. Thus, we have for every $y\in\mathbb{Z}^{d}$ the equality $\eta_{t}(y)=\sum_{x\in \mathbb{Z}^d}\eta_{x, t}(y)$ and for very $x \in\mathbb{Z}^{d}$ the equality $\eta_{x,t}=\sum_{y\in \mathbb{Z}^d}\eta_{x, t}(y)$ (subpopulation size on $\mathbb{Z}^{d}$).

The random walk of a particle on $\mathbb{Z}^{d}$ is defined by an infinitesimal matrix of transition intensities $A=\bigl(a(x,y)\bigr)_{x,y\in \mathbb{Z}^{d}}$, satisfying $\sum_{y \ne x}a(x,y)=|a(x,x)|<\infty$ for all $x$, where $a(x,y)\ge 0$ for $x\ne y$ and $a(x,x)<0$. We assume that the intensities $a(x,y)$ are symmetrical and homogeneous in space: $a(x-y):=a(x,y)=a(y,x)=a(0,y-x)$. Furthermore, we suppose, 