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Persistence in a discrete-time stage-structured fungal disease model
Paul Leonard Salceanu1, Hal L Smith
1Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, USA. salceanu@mathpost.asu.edu
Journal of Biological Dynamics
|August 14, 2012
Summary
This study analyzes a fungal disease model in amphibians, establishing criteria for disease and host population persistence. It explores conditions for host extinction and disease-free states, confirming endemic disease presence.
Area of Science:
- Epidemiology
- Mathematical Biology
- Amphibian Ecology
Background:
- Fungal diseases pose significant threats to amphibian populations globally.
- Understanding disease dynamics in structured populations is crucial for conservation.
- Vertical transmission plays a role in pathogen persistence.
Purpose of the Study:
- To analyze a discrete-time susceptible-infected (SI) epidemic model for fungal disease spread in amphibians.
- To establish criteria for the persistence of both the amphibian host population and the fungal disease.
- To investigate the stability of host extinction and disease-free equilibria and the existence of endemic equilibria.
Main Methods:
- Development and analysis of a discrete-time SI epidemic model.
- Application of stability analysis for equilibrium points.
- Utilizing bifurcation theory to determine conditions for endemic disease states.
Main Results:
- Criteria for the persistence of the amphibian host population and the fungal disease were established.
- Stability of host extinction and disease-free equilibria were determined.
- The existence of an endemic equilibrium was confirmed using bifurcation theory.
Conclusions:
- The model provides insights into the complex dynamics of fungal diseases in structured amphibian populations.
- Conditions for disease persistence and host survival can be mathematically defined.
- Bifurcation analysis confirms that endemic states are possible under specific transmission parameters.
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