Spatial dispersal in chemostat systems with agent-based asymmetry

Abstract

This paper considers chemostat consumer-resource systems in which the consumer disperses between spatial patches and acts as an agent. Using the theory of dynamical systems and the method of graphs, we demonstrate global stability of steady states in the model. It is shown that dispersal of the consumer and clustering mode of patches are important for persistence of the consumer, while asymmetry in the dispersal determines the final distribution of consumer in the system. Moreover, appropriate asymmetry could make the consumer persist in sink patches, and could make the consumer approach a total population abundance higher than that without dispersal. A novel finding of this work is that agent-based selection on asymmetry could make the consumer evolve to the maximal abundance. Numerical simulations on the model reproduce radiograph/CT of COVID-19 patients in both figures and animations. Our research has potential applications in computer-aided diagnosis and treatment.