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In this paper, we develop a stochastic Asymptotic-Preserving (sAP) scheme forthe kinetic chemotaxis system with random inputs, which will converge to themodified Keller-Segel model with random inputs in the diffusive regime. Basedon the generalized Polynomial Chaos (gPC) approach, we design a high orderstochastic Galerkin method using implicit-explicit (IMEX) Runge-Kutta (RK) timediscretization with a macroscopic penalty term. The new schemes improve theparabolic CFL condition to a hyperbolic type when the mean free path is small,which shows significant efficiency especially in uncertainty quantification(UQ) with multi-scale problems. The stochastic Asymptotic-Preserving propertywill be shown asymptotically and verified numerically in several tests. Manyother numerical tests are conducted to explore the effect of the randomness inthe kinetic system, in the aim of providing more intuitions for the theoreticstudy of the chemotaxis models.

A High Order Stochastic Asymptotic Preserving Scheme for Chemotaxis Kinetic Models with Random Inputs