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We introduce stochastic models of chemotaxis generalizing the deterministicKeller-Segel model. These models include fluctuations which are important insystems with small particle numbers or close to a critical point. FollowingDean's approach, we derive the exact kinetic equation satisfied by the densitydistribution of cells. In the mean field limit where statistical correlationsbetween cells are neglected, we recover the Keller-Segel model governing thesmooth density field. We also consider hydrodynamic and kinetic models ofchemotaxis that take into account the inertia of the particles and lead to adelay in the adjustment of the velocity of cells with the chemotactic gradient.We make the connection with the Cattaneo model of chemotaxis and the telegraphequation.

A stochastic Keller-Segel model of chemotaxis