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In this paper we consider kinetic and associated macroscopic models forchemotaxis on a network. Coupling conditions at the nodes of the network forthe kinetic problem are presented and used to derive coupling conditions forthe macroscopic approximations. The results of the different models arecompared and relations to a Keller-Segel model on networks are discussed. For anumerical approximation of the governing equations asymptotic preservingrelaxation schemes are extended to directed graphs. Kinetic and macroscopicequations are investigated numerically and their solutions are compared fortripod and more general networks.

Kinetic and related macroscopic models for chemotaxis on networks