An equivalence result for integral equations with application to branching processes

A theorem is proved, concerning expected values of a multitype branching process in a varying environment. The consequence of the theorem is that the branching process can be treated (in the sense of expected values) as a dynamical system with control terms. This is of importance in situations where the process serves as an abstract model of the dynamics of malignant cells for use in chemotherapy. A simple example of this kind is given. Work supported by the Polish Academy of Sciences Research Problem No. 10.4.3.01.4.