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Title: Stability and persistence in ODE models for populations with many stages
Authors: Fan, G
Lou, Y 
Thieme, HR
Wu, J
Issue Date: 2015
Source: Mathematical biosciences and engineering, 2015, v. 12, no. 4, p. 661-686
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.
Keywords: Basic reproduction number
Boundedness
Equilibria (existence, Lyapunov functions, and stability)
Extinction
Persistence
Uniqueness
Publisher: Arizona State University
Journal: Mathematical Biosciences and Engineering 
ISSN: 1547-1063
DOI: 10.3934/mbe.2015.12.661
Rights: © 2015 the Author(s), licensee AIMS Press.
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
The following publication Fan, G., Lou, Y., Thieme, H. R., & Wu, J. (2015). Stability and persistence in ODE models for populations with many stages. Mathematical Biosciences & Engineering, 12(4), 661-686 is available at https://doi.org/10.3934/mbe.2015.12.661
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