Endemic threshold results for an age-structured SIS epidemic model with periodic parameters
Endemic threshold results for an age-structured SIS epidemic model with periodic parameters
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DOI：
10.1016/j.jmaa.2013.01.044
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发表时间：
2013-06-15
影响因子：
1.3
通讯作者：
Inaba, Hisashi
中科院分区：
文献类型：
--
作者：
Kuniya, Toshikazu;Inaba, Hisashi
本文的主要贡献是得到了一类具有周期参数的年龄结构SIS流行病模型的非平凡地方病周期解的存在唯一性的阈值。在非自治Lotka-McKendrick系统弱遍历性的假设下，我们将感染种群的归一化系统表示为一个偏微分方程的初边值问题。将地方病周期解的存在性问题归结为一个作用于局部可积周期L-1值函数的Banach空间上的非线性积分算子的不动点问题.证明了积分算子在零点处的Frechet导数的谱半径对原微分方程弱周期解所对应的算子的非平凡不动点的存在唯一性起到阈值的作用。如果宿主种群的马尔萨斯参数等于零，则我们的阈值等于众所周知的流行病学阈值，即基本繁殖数R-0。然而，如果不是这样，那么两个阈值是不同的，我们必须关注它们的实际生物学含义。(C)2013 Elsevier Inc.保留所有权利。
The main contribution of this paper is to obtain a threshold value for the existence and uniqueness of a nontrivial endemic periodic solution of an age-structured SIS epidemic model with periodic parameters. Under the assumption of the weak ergodicity of a non-autonomous Lotka-McKendrick system, we formulate a normalized system for an infected population as an initial boundary value problem of a partial differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on a Banach space of locally integrable periodic L-1-valued functions. We prove that the spectral radius of the Frechet derivative of the integral operator at zero plays the role of a threshold for the existence and uniqueness of a nontrivial fixed point of the operator corresponding to a nontrivial periodic solution of the original differential equation in a weak sense. If the Malthusian parameter of the host population is equal to zero, our threshold value is equal to the well-known epidemiological threshold value, the basic reproduction number R-0. However, if it is not the case, then two threshold values are different from each other and we have to pay attention on their actual biological implications. (C) 2013 Elsevier Inc. All rights reserved.