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Multihost, multiparasite systems: an application of bifurcation theory
1Department of Computing Science and Mathematics, University of Stirling, Scotland, UK. j.v.greenman@stir.ac.uk
IMA Journal of Mathematics Applied in Medicine and Biology
|February 12, 2000
Summary
This study introduces a novel bifurcation theory approach to analyze complex multihost, multiparasite models, overcoming algebraic intractability without simplifying the models. The method maps system behaviors across parameter space, revealing competition dynamics and coexistence conditions.
Area of Science:
- Ecology
- Mathematical Biology
- Epidemiology
Background:
- Multihost, multiparasite models are algebraically intractable, limiting analysis.
- Previous approaches involved numerical simulations or model simplification.
- A new analytical method is needed to understand complex host-parasite interactions.
Purpose of the Study:
- To develop a new analytical approach for multihost multiparasite models using bifurcation theory.
- To analyze the equilibrium structure and qualitative properties of these models.
- To provide a framework for understanding competition and coexistence in host-parasite systems.
Main Methods:
- Utilized bifurcation theory to map model equilibrium structures in parameter space.
- Applied the approach to a two-host shared microparasite (S-I) model.
- Applied the approach to a single-host two-microparasite (S-I) model.
Main Results:
- The bifurcation theory approach avoids model simplification and dimensionality reduction.
- Map arrays provide a comprehensive catalogue of system behaviors and behavioral changes.
- Explained why previous conjectures about model behavior were not universally applicable.
- Identified conditions for collusive and competitive parasite behavior in the two-parasite model.
Conclusions:
- Bifurcation theory offers a powerful, tractable method for analyzing complex host-parasite dynamics.
- The map array visualization simplifies understanding of intricate ecological interactions.
- This approach enhances predictions of parasite competition and coexistence in ecological systems.