Numerical Solution of Transport Equations for Bacterial Chemotaxis: Effect of Discretization of Directional Motion

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Abstract
A mathematical model proposed by Alt [J. Math. Biol., 9 (1980), pp. 147–177] to describe chemotactic bacterial migration is studied, and solutions to this model are compared to solutions of a simpler model proposed by Rivero et al. [Chemical Engineering Science, 44 (1989), pp. 2881–2897]. It is found that a discretized version of Alt’s model produces solutions similar to the continuous model, even at very coarse discretization. The relationship between the discretized Alt model and the model of Rivero et al. is elucidated, and it is found that a slightly modified version of the Rivero et al. model produces solutions similar to those of the Alt model for systems with one- and two-dimensional attractant gradients, suggesting that the simple and easy-to-use Rivero et al. model (after slight modification) is adequate for modeling bacterial behavior within the parameter ranges investigated. A preliminary investigation of the use of the lattice Boltzmann method for the study of bacterial migration is reported.

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