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URN: urn:nbn:de:kobv:517-opus-51694
URL: http://opus.kobv.de/ubp/volltexte/2011/5169/

Méléard, Sylvie ; Roelly, Sylvie

A host-parasite multilevel interacting process and continuous approximations

Dokument 1.pdf (426 KB) (SHA-1:a7a238023cf66be61068c62b6f4c50624f10eea6)

Kurzfassung in Englisch

We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in these individuals. The ecological parameters of the individual dynamics depend on the number of cells of each type contained by the individual and the cell dynamics depends on the trait of the invaded individual. Our models are rooted in the microscopic description of a random (discrete) population of individuals characterized by one or several adaptive traits and cells characterized by their type. The population is modeled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation and death for individuals and birth and death for cells. The interaction between individuals (resp. between cells) is described by a competition between individual traits (resp. between cell types). We look for tractable large population approximations. By combining various scalings on population size, birth and death rates and mutation step, the single microscopic model is shown to lead to contrasting nonlinear macroscopic limits of different nature: deterministic approximations, in the form of ordinary, integro- or partial differential equations, or probabilistic ones, like stochastic partial differential equations or superprocesses. The study of the long time behavior of these processes seems very hard and we only develop some simple cases enlightening the difficulties involved.

Freie Schlagwörter (Englisch): two-level interacting processes , birth-death-mutation-competition point process , host-parasite stochastic particle system
RVK - Regensburger Verbundklassifikation: SI 990
Collection: Universität Potsdam / Aufsätze (Pre- und Postprints) / Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik / Wahrscheinlichkeitstheorie
Institut: Institut für Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: c Preprint (Vorabdruck)
Schriftenreihe: Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint / Institut für Mathematik
Bandnummer: 2011, 01
Sprache: Englisch
Erstellungsjahr: 2011
Publikationsdatum: 01.04.2011
Lizenz: Diese Nutzungsbedingung gilt nicht, wenn in den Metadaten eine modifizierende Lizenz genannt ist. Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht

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