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arXiv · 2510.15646

Derivation and quasi-invariant asymptotics of phenotype-structured integro-differential models

Emanuele Bernardi·Tommaso Lorenzi·Andrea Tosin
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Abstract

Building upon kinetic theory approaches for mass-varying multi-agent systems, we develop a modelling framework for phenotype-structured populations that makes it possible to bridge individual-level mechanisms with population-scale evolutionary dynamics. We start by formulating a stochastic agent-based model, which describes the dynamics of single population members undergoing proliferation, death, and phenotype changes. Then, we formally derive the corresponding mesoscopic model, which consists of an integro-differential equation for the distribution of population members over the space of phenotypes, where phenotype changes are modelled via an integral kernel. Finally, considering a quasi-invariant regime of small but frequent phenotype changes, we rigorously derive a non-local Fokker-Planck-type equation counterpart of this model, wherein phenotype changes are taken into account by an advection-diffusion term. The theoretical results obtained are illustrated through a sample of results of numerical simulations.

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Emanuele Bernardi, Tommaso Lorenzi, Andrea Tosin. 2025-10-17. Derivation and quasi-invariant asymptotics of phenotype-structured integro-differential models. https://arxiv.org/abs/2510.15646

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