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arXiv · 1707.03489

Global stability properties of renewal epidemic models

Michael T. Meehan·Daniel G. Cocks·Johannes Müller·Emma S. McBryde
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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, $\tau$, 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, $R_0$, represents a sharp threshold parameter such that for $R_0\leq 1$, the infection-free equilibrium is globally asymptotically stable; whereas the endemic equilibrium becomes globally asymptotically stable when $R_0 > 1$, i.e. when it exists.

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Michael T. Meehan, Daniel G. Cocks, Johannes Müller, Emma S. McBryde. 2017-07-11. Global stability properties of renewal epidemic models. https://arxiv.org/abs/1707.03489

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