Structured population models on Polish spaces: a unified approach including graphs, Riemannian manifolds and measure spaces to describe dynamics of heterogeneous populations
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes appear in a variety of applications, such as crowd dynamics, tissue regeneration, cancer development and coagulation-fragmentation...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
January 2024
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| In: |
Mathematical models and methods in applied sciences (M 3 AS)
Year: 2024, Volume: 34, Issue: 01, Pages: 109-143 |
| ISSN: | 1793-6314 |
| DOI: | 10.1142/S0218202524400037 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1142/S0218202524400037 Verlag, lizenzpflichtig, Volltext: https://www.worldscientific.com/doi/10.1142/S0218202524400037 
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| Author Notes: | Christian Düll, Piotr Gwiazda, Anna Marciniak-Czochra, Jakub Skrzeczkowski |
| Summary: | This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes appear in a variety of applications, such as crowd dynamics, tissue regeneration, cancer development and coagulation-fragmentation processes. The diverse applications pose a common challenge to mathematicians due to the multiscale nature of the structures that underlie the system’s self-organization and control. Similar abstract mathematical problems arise when formulating problems in the language of measure evolution on a multi-faceted state space. Motivated by these observations, we propose a general mathematical framework for nonlinear structured population models on abstract metric spaces, which are only assumed to be separable and complete. We exploit the structure of the space of non-negative Radon measures with the dual bounded Lipschitz distance (flat metric), which is a generalization of the Wasserstein distance, capable of addressing non-conservative problems. The formulation of models on general metric spaces allows considering infinite-dimensional state spaces or graphs and coupling discrete and continuous state transitions. This opens up exciting possibilities for modeling single-cell data, crowd dynamics or coagulation-fragmentation processes. |
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| Item Description: | Veröffentlicht: 8 November 2023 Gesehen am 11.03.2024 |
| Physical Description: | Online Resource |
| ISSN: | 1793-6314 |
| DOI: | 10.1142/S0218202524400037 |