Mathematical Modeling of Bacterial Motion with Stochastic Reversals



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Commonly, models describing bacteria use an Exponential distribution to describe the reversal time of the bacteria. However, experimental evidence shows that the reversal time more accurately follows a Gamma distribution. Therefore, we perform the analysis of experimental data on the reversal time and the speed of propagation of bacteria inside and outside of the aggregate. Use that data to build multiple agent-based models, and in each model, compare the effects of Gamma and Exponential reversal times. We identified that the most simple model has similar trends to the most complex model, and therefore solve for the exact stationary distribution and numerical PDE approximation of the stationary distribution for that model. Finally, we verify the simulations by comparing them to those solutions.



Mathematical Modeling, Myxococcus Xanthus