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.

Modelling the effect of birth and feeding modes on the development of human gut microbiota

“…Increased strength of competition leads to the divergence of microbial profile following different birth environments. The divergent outcomes are owing to bistability in the dynamics, which was also observed in studies that model commensalpathogen competition [46] and microbe-immune system interaction [54]. Variation in post-weaning Bifidobacteria abundance in response to different birth and feeding modes cannot be produced by competition alone.…”

“…The effects of initial colonization on the competitive outcome between an invasive and a commensal gut population have been studied with chemostat models [44,45] and a recent Lotka-Volterra-type ecological model [46]. The prevalence of competition has been shown in ecological network models [1,47] and human gut community interaction topologies [48,49].…”

Interplay between COVID-19 vaccines and social measures for ending the SARS-CoV-2 pandemic

“…The third boundary condition is equivalent to ( ) c I τ ′ = 0 and therefore requires I c to be at a local maximum at time τ. The variable τ is therefore the time at which I c reaches its maximum 16 . Evaluating I c at t = τ for any solution of BVP ( 3)-( 5) provides the peak ICU cases for the fixed parameter set.…”

Interplay between COVID-19 vaccines and social measures for ending the SARS-CoV-2 pandemic

“…The third boundary condition is equivalent to ( ) c I τ ′ = 0 and therefore requires I c to be at a local maximum at time τ. The variable τ is therefore the time at which I c reaches its maximum 17 . Evaluating I c at t = τ for any solution of BVP ( 3)-( 5) provides the peak ICU cases for the fixed parameter set.…”