Global stability properties of a class of renewal epidemic models

Meehan, Michael T.;Cocks, Daniel G.;Mueller, Johannes;McBryde, Emma S.

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.

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Journal of Mathematical Biology

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1432-1416

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Springer

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DOI

10.1007/s00285-018-01324-1