A class of branching processes with two dependent types (Q806182)

To describe a host parasite relationship, a two type branching process is constructed. The peculiarity here is that type I individuals enter the population by immigration and type II individuals are generated by type I ancestors. The later may affect the life of the former and, once a type I individual dies, all of its type II descendants die as well. After going through the construction of such process, the authors compute the distributions of several random variables measuring different population sizes, and, under the assumptions of a limiting immigration intensity and finite mean life of individuals of type I, they obtain the stationary distributions of the relevant population sizes.