Generalized Keller-Segel models of chemotaxis. Analogy with nonlinear mean field Fokker-Planck equations

Abstract: We consider a generalized class of Keller-Segel models describing the chemotaxis of biological populations (bacteria, amoebae, endothelial cells, social insects,...). We show the analogy with nonlinear mean field Fokker-Planck equations and generalized thermodynamics. As an illustration, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion principle (volume filling). We also discuss the analogy between biological populations described by the Keller-Segel model and self-gravitating Brownian particles described by the Smoluchowski-Poisson system.