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Global Properties of Infectious Disease Models with Nonlinear Incidence
| Title: | Global Properties of Infectious Disease Models with Nonlinear Incidence |
| Authors: | Korobeinikov, Andrei Browse this author |
| Keywords: | Direct Lyapunov method | | Lyapunov function | | Endemic equilibrium state | | Global stability | | Nonlinear incidence |
| Issue Date: | Aug-2007 |
| Publisher: | Springer New York |
| Journal Title: | Bulletin of Mathematical Biology |
| Volume: | 69 |
| Issue: | 6 |
| Start Page: | 1871 |
| End Page: | 1886 |
| Publisher DOI: | 10.1007/s11538-007-9196-y |
| PMID: | 17443392 |
| Abstract: | We consider global properties for the classical SIR, SIRS and SEIR models of infectious diseases, including the models with the vertical transmission, assuming that the horizontal transmission is governed by an unspecified function f(S,I). We construct Lyapunov functions which enable us to find biologically realistic conditions sufficient to ensure existence and uniqueness of a globally asymptotically stable equilibrium state. This state can be either endemic, or infection-free, depending on the value of the basic reproduction number. |
| Rights: | The original publication is available at
www.springerlink.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/30189 |
| Appears in Collections: | 電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: Andrei Korobeinikov
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