title: A stochastic model for immunotherapy of cancer.
abstract: We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context the different actors, T-cells, cytokines or cancer cells, are modelled as single particles (individuals) in the stochastic system. The main expansions of the model are distinguishing cancer cells by phenotype and genotype, including environment-dependent phenotypic plasticity that does not affect the genotype, taking into account the effects of therapy and introducing a competition term which lowers the reproduction rate of an individual in addition to the usual term that increases its death rate. We illustrate the new setup by using it to model various phenomena arising in immunotherapy. Our aim is twofold: on the one hand, we show that the interplay of genetic mutations and phenotypic switches on different timescales as well as the occurrence of metastability phenomena raise new mathematical challenges. On the other hand, we argue why understanding purely stochastic events (which cannot be obtained with deterministic models) may help to understand the resistance of tumours to therapeutic approaches and may have non-trivial consequences on tumour treatment protocols. This is supported through numerical simulations.
authors.affiliation: Institute for Applied Mathematics, Bonn University, Bonn, Germany.
authors.forename: Martina
authors.initials: M
authors.lastname: Baar
authors.affiliation: Institute for Applied Mathematics, Bonn University, Bonn, Germany.
authors.forename: Loren
authors.initials: L
authors.lastname: Coquille
authors.affiliation: Institute for Applied Mathematics, Bonn University, Bonn, Germany.
authors.forename: Hannah
authors.initials: H
authors.lastname: Mayer
authors.affiliation: Institute for Clinical Chemistry and Clinical Pharmacology, University Hospital, Bonn University, Bonn, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Hölzel
authors.affiliation: Laboratory of Experimental Dermatology, Department of Dermatology and Allergy, University Hospital, Bonn University, Bonn, Germany.
authors.forename: Meri
authors.initials: M
authors.lastname: Rogava
authors.affiliation: Laboratory of Experimental Dermatology, Department of Dermatology and Allergy, University Hospital, Bonn University, Bonn, Germany.|Department of Dermatology, University Hospital, Magdeburg University, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Tüting
authors.affiliation: Institute for Applied Mathematics, Bonn University, Bonn, Germany.
authors.forename: Anton
authors.initials: A
authors.lastname: Bovier
mesh_terms: D005838:Genotype; D006801:Humans; D007167:Immunotherapy; D008962:Models, Theoretical; D009154:Mutation; D009369:Neoplasms / Q000401:mortality / Q000628:therapy*; D013269:Stochastic Processes