Format

Send to

Choose Destination
J Math Biol. 2019 May;78(6):1713-1725. doi: 10.1007/s00285-018-01324-1. Epub 2019 Feb 9.

Global stability properties of a class of renewal epidemic models.

Author information

1
Australian Institute of Tropical Health and Medicine, James Cook University, Townsville, Australia. michael.meehan1@jcu.edu.au.
2
Research School of Science and Engineering, Australian National University, Canberra, Australia.
3
Centre for Mathematical Sciences, Technische Universität München, and Institute of Computational Biology, German Research Center for Environmental Health, München, Germany.
4
Australian Institute of Tropical Health and Medicine, James Cook University, Townsville, Australia.

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, [Formula: see text], 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, [Formula: see text], represents a sharp threshold parameter such that for [Formula: see text], the infection-free equilibrium is globally asymptotically stable; whereas the endemic equilibrium becomes globally asymptotically stable when [Formula: see text], i.e. when it exists.

KEYWORDS:

Global stability; Kermack–McKendrick; Lyapunov; Renewal

PMID:
30737545
DOI:
10.1007/s00285-018-01324-1

Supplemental Content

Full text links

Icon for Springer
Loading ...
Support Center