Chemotaxis–Reaction Models in Microbial Ecology: Theory, Analysis, and Applications

Chemotaxis, the directed movement of microorganisms in response to chemical gradients, plays a pivotal role in microbial ecology. This article provides a comprehensive review of mathematical models that couple chemotaxis with reaction dynamics to describe microbial population behavior. We discuss how such chemotaxis–reaction models capture essential ecological phenomena, from nutrient foraging and biofilm formation to inter-species competition and environmental processes. Key model formulations, starting from the classical Keller--Segel system, are presented alongside extensions incorporating multiple species, complex reaction terms, and fluid flow coupling. We survey rigorous mathematical results on well-posedness, pattern formation, and stability, highlighting analytical tools in partial differential equations (PDEs) and functional analysis. Numerical simulation techniques are reviewed, illustrating how computational methods can capture chemotactic pattern formation. Biological applications are emphasized throughout, drawing connections between model predictions and experimental observations of bacterial aggregation patterns, biofilm spatial structure, and microbial competition. Finally, we outline open problems and future directions, including stochastic modeling, multiscale approaches, and data-driven techniques, underscoring the interdisciplinary outlook. The contributions of this article lie in synthesizing recent advances in chemotaxis–reaction modeling and analysis, and in elucidating the interplay between theory and experiment in microbial ecology.