Global stability properties of a class of renewal epidemic models
Meehan, Michael T., Cocks, Daniel G., Mueller, Johannes, and McBryde, Emma S. (2019) Global stability properties of a class of renewal epidemic models. Journal of Mathematical Biology, 78 (6). pp. 1713-1725.
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Abstract
We investigate the global dynamics of a general Kermack-McKendrick-type epidemic model formulated in terms of a system of renewal equations. Specifically, we consider a renewal model for which both the force of infection and the infected removal rates are arbitrary functions of the infection age, , and use the direct Lyapunov method to establish the global asymptotic stability of the equilibrium solutions. In particular, we show that the basic reproduction number, R0, represents a sharp threshold parameter such that for R01, the infection-free equilibrium is globally asymptotically stable; whereas the endemic equilibrium becomes globally asymptotically stable when R0>1, i.e. when it exists.
| Item ID: | 58286 |
|---|---|
| Item Type: | Article (Research - C1) |
| ISSN: | 1432-1416 |
| Keywords: | Global stability, Lyapunov, Renewal, Kermack-McKendrick |
| Copyright Information: | © Springer-Verlag GmbH Germany, part of Springer Nature 2019 |
| Date Deposited: | 15 May 2019 07:47 |
| FoR Codes: | 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490102 Biological mathematics @ 50% 42 HEALTH SCIENCES > 4202 Epidemiology > 420204 Epidemiological methods @ 50% |
| SEO Codes: | 92 HEALTH > 9204 Public Health (excl. Specific Population Health) > 920404 Disease Distribution and Transmission (incl. Surveillance and Response) @ 100% |
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