Meehan, Michael T.Cocks, DanielMüller, JohannesMcBryde, Emma2020-06-250303-6812http://hdl.handle.net/1885/205557We 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, τ , 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 R0≤1 , the infection-free equilibrium is globally asymptotically stable; whereas the endemic equilibrium becomes globally asymptotically stable when R0>1 , i.e. when it exists.application/pdfen-AU© Springer-Verlag GmbH Germany, part of Springer Nature 2019201910.1007/s00285-018-01324-12020-01-19