Persistence in a discrete-time stage-structured fungal disease model

Abstract

A discrete-time susceptible and infected (SI) epidemic model, with less than 100% vertical disease transmission, for the spread of a fungal disease in a structured amphibian host population, is analysed. Criteria for persistence of the population as well as the disease are established. Stability results for host extinction and for the disease-free equilibrium are presented. Bifurcation theory is used to establish existence of an endemic equilibrium.

Keywords:

• structured populations
• SI epidemic model
• persistence
• vertical transmission
• bifurcation

AMS Clasification :

• 39A11
• 92D30

Acknowledgements

Financial support was provided by a National Science Foundation Grant, DMS 0414270. The authors would like to acknowledge the useful comments of the reviewers.