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Global stability properties of a class of renewal epidemic models
Michael T Meehan1, Daniel G Cocks2, Johannes Müller3
1Australian Institute of Tropical Health and Medicine, James Cook University, Townsville, Australia. michael.meehan1@jcu.edu.au.
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.
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