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Localization and Extinction of Bacterial Populations under Inhomogeneous Growth Conditions

Center for Nonlinear Dynamics and Department of Physics, The University of Texas, Austin, Texas 78712

Correspondence: Address reprint requests to Anna L. Lin, E-mail: alin{at}phy.duke.edu.

The transition from localized to systemic spreading of bacteria, viruses, and other agents is a fundamental problem that spans medicine, ecology, biology, and agriculture science. We have conducted experiments and simulations in a simple one-dimensional system to determine the spreading of bacterial populations that occurs for an inhomogeneous environment under the influence of external convection. Our system consists of a long channel with growth inhibited by uniform ultraviolet (UV) illumination except in a small "oasis", which is shielded from the UV light. To mimic blood flow or other flow past a localized infection, the oasis is moved with a constant velocity through the UV-illuminated "desert". The experiments are modeled with a convective reaction-diffusion equation. In both the experiment and model, localized or extinct populations are found to develop, depending on conditions, from an initially localized population. The model also yields states where the population grows everywhere. Further, the model reveals that the transitions between localized, extended, and extinct states are continuous and nonhysteretic. However, it does not capture the oscillations of the localized population that are observed in the experiment.