https://doi.org/10.1140/epjp/s13360-021-01692-6
Regular Article
New traveling waves for a (2 + 1)-dimensional chemotactic system with uniform flow
1
Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
2
African Centre for Advanced Studies, P.O. Box 4477, Yaounde, Cameroon
3
Department of Mathematics and Physical Sciences, National Advanced School of Engineering of Yaounde, University of Yaounde I, P.O. Box 8390, Yaounde, Cameroon
4
National Advanced School of Engineering of Maroua, University of Maroua, P.O. Box 46, Maroua, Cameroon
Received:
20
April
2021
Accepted:
22
June
2021
Published online:
29
June
2021
Traveling waves propagating in a two-dimensional advection-chemotactic system in the presence of constant growth and chemoattractant consumption rates are addressed in the present paper. The advection rate is induced by the flow of the fluid within which bacteria are immersed. The traveling wave transformation allows us to reduce the model to a nonlinear ordinary differential equation which is solved by means of an extended F-expansion method. Families of analytical solutions for bacterial density-chemoattractant concentration uncovered exhibit some important characteristics. The critical value of the advection rate in one direction derived shows that it is proportional to the ratio of the wave’s widths in both spatial directions in addition to the advection rate in the orthogonal direction. In this case, solutions are stationary. Above that critical value, the fluid flow rate interacts constructively with the chemotactic motion of bacteria and favors their convergence towards the food source. Below the critical value of the advection rate, the chemotactic motion is counteracted by the flow rate which tends to sweep bacteria and/or swerve the bacterial motion. Further, reducing chemoattractant consumption rate and the medium carrying capacity leads to both wave thickness and amplitude increase, with the consequence of optimizing both spatial repartition and the number of cells carried by the wave. Intensive numerical simulations performed with parameters closed to experimental ones of the original set of model equations corroborate their analytical counterparts with good accuracy, hence paving the way towards the realization of our predictions in current or future experiments
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-021-01781-6.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
