Mean-Field Limits and the Multiscale Approach to Cell Movements

Explore a mathematical lecture on hybrid models for collective cell movement under chemical stimuli and their macroscopic counterparts. Delve into the mean-field limit theory for discrete particle systems where cells are governed by ordinary differential equations while chemoattractants follow continuous diffusive equations. Learn how to prove convergence in Wasserstein distance to coupled Vlasov-type equations with chemoattractant dynamics, using marginals of individual densities rather than empirical measures. Discover explicit bounds for the limit process and examine existence and uniqueness proofs for the resulting system. Investigate the derivation of pressureless nonlocal Euler-type models with chemotaxis in monokinetic cases and compare these with other macroscopic approaches to cell movement modeling. Gain insights into the multiscale mathematical framework that bridges discrete cellular behavior with continuous population dynamics in biological systems.