Persistence in a discrete-time, stage-structured epidemic model

Abstract

Discrete-time SI and SIR epidemic models, formulated by Emmert and Allen [J. Differ. Equ. Appl., 10 (2004), pp. 1177–1199] for the spread of a fungal disease in a structured amphibian host population, are analysed. Criteria for persistence of the population as well as for persistence of the disease are established. Global stability results for host extinction and for the disease-free equilibrium are presented.

Keywords:

• structured populations
• SIR epidemic model
• persistence
• global stability

Acknowledgements

Financial support was provided by a National Science Foundation Grant, DMS 0414270. We thank Linda Allen for useful comments.