Waiting for a Mathematical Theory of Living Systems from a Critical Review to Research Perspectives

Burini, Diletta; Chouhad, Nadia; Bellomo, Nicola

doi:10.3390/sym15020351

Cited by 7 publications

(1 citation statement)

References 57 publications

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“…This perspective applies to self-propelled particles such as human crowds [7,8]. These models, as reviewed in [5,21], can take into account various aspects of the heterogeneity and evolutive features of living systems.…”

Section: Oncolytic Virus Model In a Cross Diffusion Systemmentioning

confidence: 99%

Cross diffusion models in complex frameworks From microscopic to macroscopic

Burini¹,

Chouhad²

2023

Preprint

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This paper deals with the micro-macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the so-called exotic models according to the definition proposed in in [9]. The first part of the presentation focuses on a survey and a critical analysis of some phenomenological models known in the literature. We refer to a selection of case studies, in detail: transport of virus models, social dynamics, and Keller-Segel in a fluid. The second part shows how an Hilbert type approach can be developed to derive models at the macroscale from the underlying description provided by the kinetic theory of active particles. The third part deals with the derivation of macroscopic models corresponding to the selected case studies. Finally, a forward look into the future research perspectives is proposed.

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Section: Oncolytic Virus Model In a Cross Diffusion Systemmentioning

confidence: 99%

Cross diffusion models in complex frameworks From microscopic to macroscopic

Burini¹,

Chouhad²

2023

Preprint

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Parrondo's paradox reveals counterintuitive wins in biology and decision making in society

Wen,

Cheong

2024

Physics of Life Reviews

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A nonconservative kinetic framework under the action of an external force field: Theoretical results with application inspired to ecology

Carbonaro,

Menale

2023

Eur. J. Appl. Math

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The present paper deals with the kinetic-theoretic description of the evolution of systems consisting of many particles interacting not only with each other but also with the external world, so that the equation governing their evolution contains an additional term representing such interaction, called the ‘forcing term’. Firstly, the interactions between pairs of particles are both conservative and nonconservative; the latter represents, among others, birth/death rates. The ‘forcing term’ does not express a ‘classical’ force exerted by the external world on the particles, but a more general influence on the effects of mutual interactions of particles, for instance, climate changes, that increase or decrease the different agricultural productions at different times, thus altering the economic relationships between different subsystems, that in turn can be also perturbed by stock market fluctuations, sudden wars, periodic epidemics, and so on. Thus, the interest towards these problems moves the mathematical analysis of the effects of different kinds of forcing terms on solutions to equations governing the collective (that is statistical) behaviour of such nonconservative many-particle systems. In the present paper, we offer a study of the basic mathematical properties of such solutions, along with some numerical simulations to show the effects of forcing terms for a classical prey–predator model in ecology.

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Waiting for a Mathematical Theory of Living Systems from a Critical Review to Research Perspectives

Cited by 7 publications

References 57 publications

Cross diffusion models in complex frameworks From microscopic to macroscopic

Cross diffusion models in complex frameworks From microscopic to macroscopic

Parrondo's paradox reveals counterintuitive wins in biology and decision making in society

A nonconservative kinetic framework under the action of an external force field: Theoretical results with application inspired to ecology

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