[@VC:04]. The latent stage is also presented in the construction of propagation strategy of some bacteriophages [@CMLH:11]. Here, until the infected cell remains in an unfriendly environment, virus does not kill it, inherits by filial cells and integrates into the cell’s genome. But when the infected bacteria enters a favorable environment, the infectious agent captures the control over cell’s processes and it begins to produce materials for building new viral particles. Thousands of them move out of the cell, break the membrane, leading the cell’s death. With virus persistence (for example, papovaviruses) some oncological diseases are related, see, e.g., [@B:96].

In the above mentioned BRW model with an infinite number of initial particles every particle at a point of the lattice at initial time could present a virus in the latent stage. Then the branching source is a place with a favorable environment for the disease progression. Getting into it, the virus enter the active stage from the latency, so the transmission and the infection of other members of the population become possible.

Both of the BRW models can be considered taking into account the vaccination process. Unlike to [@GMS-B:10], we suppose the vaccination to be presented by a reduced 