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An equivalence result for integral equations with application to branching processes

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Abstract

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.

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Authors and Affiliations

  1. Institute of Automation, Silesian Technical University, Pstrowskiego 16, 44-100, Gliwice, Poland

    Marek Kimmel

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  1. Marek Kimmel
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Work supported by the Polish Academy of Sciences Research Problem No. 10.4.3.01.4.

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Kimmel, M. An equivalence result for integral equations with application to branching processes. Bltn Mathcal Biology 44, 1–15 (1982). https://doi.org/10.1007/BF02459415

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  • DOI: https://doi.org/10.1007/BF02459415

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