Critical multitype branching processes on a graph and the model of the HIV infection development

Аннотация

We consider the Crump-Mode-Jagers branching process
on an oriented graph in an application to modeling the development
of HIV-1 infection in a human organism. For all particles of the same
global type, located at each of the vertexes or arcs of the graph, different
types are assigned. Checking the criticality condition and searching for
the eigenvectors of an offspring mean matrix in the critical case for the
original process are reduced to an offspring mean matrix for some Galton-
Watson process. The last has the types of particles corresponding only
to the vertexes of the graph.