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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 |
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 |
| Appears in Collections: | Journal/Magazine Article |
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| Fan_Stability_Persistenceode_Models.pdf | 393.31 kB | Adobe PDF | View/Open |
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