Regime switching on the propagation speed of travelling waves of some size-structured myxobacteria population models
ESAIM. Proceedings, Tome 77 (2024), pp. 195-212
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The spatial propagation of complex populations can depend on some structuring variables. In particular, recent developments in microscopy have revealed the impact of bacteria heterogeneity on the population motility. Biofilms of Myxococcus xanthus bacteria have been shown to be structured in clusters of various sizes, which remarkably, tend to move faster when they consist of a larger number of bacteria. We propose a minimal reaction-diffusion discrete-size structure model of a population of Myxococcus with two possible cluster sizes: isolated and paired bacteria. Numerical experiments show that this model exhibits travelling waves whose propagation speed depends on the increased motility of clusters, and the exchange rates between isolated bacteria and clusters. Notably, we present evidence of the existence of a characteristic threshold level θ*. on the ratio between cluster motility and isolated bacteria motility, which separates two distinct regimes of propagation speed. When the ratio is less or equal than θ*, the propagation speed of the population is constant with respect to the ratio. However, when the ratio is above θ*, the propagation speed increases. We also consider a generalised model with continuous-size structure, which also shows the same behaviour. We extend the model to include interactions with a resource population, which show qualitative behaviours in agreement to the biological experiments.
Affiliations des auteurs :
Vincent Calvez 1 ; Adil El Abdouni 2 ; Maxime Estavoyer 1 ; Ignacio Madrid 3 ; Julien Olivier 4 ; Magali Tournus 4
@article{EP_2024_77_a9,
author = {Vincent Calvez and Adil El Abdouni and Maxime Estavoyer and Ignacio Madrid and Julien Olivier and Magali Tournus},
title = {Regime switching on the propagation speed of travelling waves of some size-structured myxobacteria population models},
journal = {ESAIM. Proceedings},
pages = {195--212},
year = {2024},
volume = {77},
doi = {10.1051/proc/202477195},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202477195/}
}
TY - JOUR AU - Vincent Calvez AU - Adil El Abdouni AU - Maxime Estavoyer AU - Ignacio Madrid AU - Julien Olivier AU - Magali Tournus TI - Regime switching on the propagation speed of travelling waves of some size-structured myxobacteria population models JO - ESAIM. Proceedings PY - 2024 SP - 195 EP - 212 VL - 77 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202477195/ DO - 10.1051/proc/202477195 LA - en ID - EP_2024_77_a9 ER -
%0 Journal Article %A Vincent Calvez %A Adil El Abdouni %A Maxime Estavoyer %A Ignacio Madrid %A Julien Olivier %A Magali Tournus %T Regime switching on the propagation speed of travelling waves of some size-structured myxobacteria population models %J ESAIM. Proceedings %D 2024 %P 195-212 %V 77 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202477195/ %R 10.1051/proc/202477195 %G en %F EP_2024_77_a9
Vincent Calvez; Adil El Abdouni; Maxime Estavoyer; Ignacio Madrid; Julien Olivier; Magali Tournus. Regime switching on the propagation speed of travelling waves of some size-structured myxobacteria population models. ESAIM. Proceedings, Tome 77 (2024), pp. 195-212. doi: 10.1051/proc/202477195
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