Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/24088
Title: Stability and persistence in ODE models for populations with many stages
Authors: Fan, G
Lou, Y 
Thieme, HR
Wu, J
Keywords: Basic reproduction number
Boundedness
Equilibria
Extinction
Lyapunov functions
Persistence
Uniqueness
Issue Date: 2015
Publisher: Arizona State University
Source: Mathematical biosciences and engineering, 2015, v. 12, no. 4, p. 661-686 How to cite?
Journal: Mathematical Biosciences and Engineering 
Abstract: A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.
URI: http://hdl.handle.net/10397/24088
ISSN: 1547-1063
DOI: 10.3934/mbe.2015.12.661
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