title: A Boundary Value Approach to Optimization with an Application to Salmonella Competition.
abstract: We develop a novel optimization framework to study strategies in ecological competition processes. The optimization method uses theory from dynamical systems describing the asymptotic behavior of a bistable system based on initial conditions, which we implement using a numerical boundary value problem. As an application of our method, we develop a model of the competition between Salmonella Typhimurium and the host's native microflora, which constantly and densely inhabit the intestinal lining of most mammals. S. Typhimurium invades the gut in two distinct phenotypic populations, one virulent and one avirulent, though the avirulent bacteria have the ability to activate a virulence factor and thereby "switch" into the virulent population. Counterintuitively, some studies have found that the combined population of S. Typhimurium gains an environmental advantage over the commensal microbiota after the virulent subpopulation provokes the body's inflammatory defenses. Our model represents the competition between the commensal microbiota, the avirulent salmonella, and the virulent salmonella populations and incorporates a simple representation of the immune response. We use our model to predict optimal strategies that would favor salmonella in its competition with the commensal bacteria.
authors.affiliation: Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA, gsy2@pitt.edu.
authors.forename: Glenn
authors.initials: G
authors.lastname: Young
authors.forename: Bard
authors.initials: B
authors.lastname: Ermentrout
authors.forename: Jonathan E
authors.initials: JE
authors.lastname: Rubin
mesh_terms: D000818:Animals; D000069196:Gastrointestinal Microbiome; D054884:Host-Pathogen Interactions; D055641:Mathematical Concepts; D008954:Models, Biological; D012486:Salmonella typhimurium / Q000472:pathogenicity*; D014774:Virulence