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Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission
| Title: | Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission |
| Authors: | Korobeinikov, Andrei Browse this author |
| Keywords: | Direct Lyapunov method | | Lyapunov function | | endemic equilibrium state | | global stability | | nonlinear incidence | | MSC=92D30 | | MSC=34D20 |
| Issue Date: | Apr-2006 |
| Publisher: | Springer New York |
| Journal Title: | Bulletin of Mathematical Biology |
| Volume: | 68 |
| Issue: | 3 |
| Start Page: | 615 |
| End Page: | 626 |
| Publisher DOI: | 10.1007/s1153S-005-9037-9 |
| Abstract: | Lyapunov functions for 2-dim SIR and SIRS compartmental epidemic models with non-linear transmission rate of a very general form f(S, I) constrained by a few biologically feasible conditions are constructed. Global properties of these models including these with vertical and horizontal transmission, are thereby established. It is proved that, under the constant population size assumption, the concavity of the function f(S, I) with respect to the number of the infective hosts I ensures the uniqueness and the global stability of the positive endemic equilibrium state. |
| Rights: | The original publication is available at www.springerlink.com |
| Relation: | http://www.springerlink.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/33886 |
| 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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