Global stability properties of a class of renewal epidemic models

Michael T Meehan, Daniel G Cocks, Johannes Müller, Emma S McBryde

Journal of mathematical biology 78 (6), 1713-1725; Global stability properties of a class of renewal epidemic models

 

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, , represents a sharp threshold parameter such that for , the infection-free equilibrium is globally asymptotically stable; whereas the endemic equilibrium becomes globally asymptotically stable when , i.e. when it exists.