2025/10/17 by Emanuele Bernardi, Tommaso Lorenzi, Bernardi, Emanuele +3
Mathematics · Medicine · Social Sciences · #35Q84 #35Q92 #35R09 #Analysis of PDEs (math.AP) #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2510.15646
openalex publication_date 2025/10/17 · openalex created_date 2025/10/21 · openalex updated_date 2026/07/28
Building upon kinetic theory approaches for multi-agent systems and generalising them to scenarios where the total mass of the system is not conserved, 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.