Séminaire des doctorants Orléans
Paguiel Hossie: Persistence and Extinction Dynamics in a Coupled Reaction-Diffusion-Convection Model with Monod-Type Growth: Application to Bacterial Growth in the ColonPaguiel Hossie (IDP-Orléans)
Thursday 03 April 2025 10:30 - IDP-Orléans - Salle de séminaire
Résumé :
Biological population dynamics are influenced by environmental interactions, movement patterns, and density-dependent growth. Reaction-diffusion-convection models help analyze these effects, particularly in advective environments. In this work, we analyze the persistence of wild-type bacterial population consuming a nutrient in a hydrodynamic flow, modeled by a reaction-diffusion-convection system with Robin type boundary conditions. Unlike classical logistic models, the bacterial growth follows a Monod-type nonlinearity, adding complexity due to the non-self-adjoint nature of the associated elliptic operator. This model, inspired by Labavić and al. "Hydrodynamic flow and concentration gradients in the gut enhance neutral bacterial diversity". Using phase plane analysis and spectral analysis, we identify a critical domain size L* that dictates bacterial survival. Our results demonstrate that for low flow velocities, bacteria systematically persist when the domain length exceeds the critical domain size, i.e., when L>L*. This work represents a first step in the mathematical study of mutant dynamics in the intestine. In this context, we consider a scenario where, at the initial time, a small population of mutants is introduced in a small localized region around a position x_M. The initial concentration of mutants at this point is very very low compared to that of wild-type bacteria.
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