Bj. Brosilow et al., NUMERICAL-SOLUTION OF TRANSPORT-EQUATIONS FOR BACTERIAL CHEMOTAXIS - EFFECT OF DISCRETIZATION OF DIRECTIONAL MOTION, SIAM journal on applied mathematics, 56(6), 1996, pp. 1639-1663
A mathematical model proposed by Alt [J. Math. Biol., 9 (1980), pp. 14
7-177] to describe chemotactic bacterial migration is studied, and sol
utions to this model are compared to solutions of a simpler model prop
osed by Rivero et al. [Chemical Engineering Science, 44 (1989), pp. 28
81-2897]. It is found that a discretized version of Alt's model produc
es solutions similar to the continuous model, even at very coarse disc
retization. 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 simila
r to those of the Alt model for systems with one- and two-dimensional
attractant gradients, suggesting that the simple and easy-to-use River
o et al. model (after slight modification) is adequate for modeling ba
cterial behavior within the parameter ranges investigated. A prelimina
ry investigation of the use of the lattice Boltzmann method for the st
udy of bacterial migration is reported.