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A Boundary Value Approach to Optimization with an Application to Salmonella Competition
Glenn Young1, Bard Ermentrout, Jonathan E Rubin
1Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA, gsy2@pitt.edu.
Bulletin of Mathematical Biology
|July 1, 2015
Summary
This study models bacterial competition, finding optimal strategies for Salmonella Typhimurium to outcompete host microflora. The framework uses dynamical systems and numerical methods to analyze invasion dynamics and immune responses.
Area of Science:
- Ecology
- Microbiology
- Mathematical Biology
Background:
- The gut microbiome plays a crucial role in host health.
- Salmonella Typhimurium competes with native microflora for intestinal colonization.
- S. Typhimurium exists in virulent and avirulent forms, with potential to switch phenotypes.
Purpose of the Study:
- To develop a novel optimization framework for studying ecological competition.
- To model the competition between Salmonella Typhimurium and the host's commensal microbiota.
- To predict strategies favoring S. Typhimurium dominance.
Main Methods:
- Utilized dynamical systems theory to describe bistable system behavior.
- Implemented a numerical boundary value problem for optimization.
- Developed a mathematical model incorporating commensal microbiota, virulent/avirulent S. Typhimurium, and immune response.
Main Results:
- The model predicts optimal strategies for S. Typhimurium in competition.
- Demonstrated how virulent subpopulations can confer an advantage despite inflammatory responses.
- Identified key factors influencing the competitive dynamics between S. Typhimurium and microflora.
Conclusions:
- The developed optimization framework is effective for ecological competition studies.
- Understanding competitive strategies is crucial for managing S. Typhimurium infections.
- The model provides insights into host-pathogen interactions and microbiome dynamics.
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