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Meehan, M.T.* ; Cocks, D.G.* ; Müller, J. ; McBryde, E.S.*

Global stability properties of a class of renewal epidemic models.

J. Math. Biol. 78, 1713-1725 (2019)

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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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