Meehan Michael T, Cocks Daniel G, Müller Johannes, McBryde Emma S
Australian Institute of Tropical Health and Medicine, James Cook University, Townsville, Australia.
Research School of Science and Engineering, Australian National University, Canberra, Australia.
J Math Biol. 2019 May;78(6):1713-1725. doi: 10.1007/s00285-018-01324-1. Epub 2019 Feb 9.
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.
我们研究了一个用更新方程系统表述的一般Kermack-McKendrick型流行病模型的全局动力学。具体而言，我们考虑一个更新模型，其中感染率和感染移除率都是感染年龄(\tau)的任意函数，并且使用直接李雅普诺夫方法建立平衡解的全局渐近稳定性。特别地，我们表明基本再生数(R_0)代表一个尖锐的阈值参数，使得当(R_0 < 1)时，无感染平衡是全局渐近稳定的；而当(R_0 > 1)时，即当地方病平衡存在时，它变得全局渐近稳定。
