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: 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010202 Biological Mathematics @ 50%
11 MEDICAL AND HEALTH SCIENCES > 1117 Public Health and Health Services > 111706 Epidemiology @ 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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