An age-structured epidemic model for the demographic transition
An age-structured epidemic model for the demographic transition
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DOI：
10.1007/s00285-018-1253-7
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发表时间：
2018-11-01
影响因子：
1.9
通讯作者：
Bacaer, Nicolas
中科院分区：
文献类型：
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作者：
Inaba, Hisashi;Saito, Ryohei;Bacaer, Nicolas
在这篇文章中，我们建立了人口转变的年龄结构流行病模型，其中我们假设导致低生育率的文化规范以与传染病相同的方式在个体之间传播。首先，我们将基本模型表示为Banach空间上的抽象齐次柯西问题，以证明解的存在唯一性和适定性。其次，基于归一化理论，我们研究了非平凡指数解的存在性，并利用异步指数增长的思想研究了非平凡指数解的线性化稳定性。考察了归一化系统的相对稳定性和原系统的绝对(轨道)稳定性。对于对应于无感染或完全感染状态的边界指数解，我们利用再生数给出了稳定性条件。我们证明了边界指数解的双不稳定性是保证共存指数解存在的条件之一。
In this paper, we formulate an age-structured epidemic model for the demographic transition in which we assume that the cultural norms leading to lower fertility are transmitted amongst individuals in the same way as infectious diseases. First, we formulate the basic model as an abstract homogeneous Cauchy problem on a Banach space to prove the existence, uniqueness, and well-posedness of solutions. Next based on the normalization arguments, we investigate the existence of nontrivial exponential solutions and then study the linearized stability at the exponential solutions using the idea of asynchronous exponential growth. The relative stability defined in the normalized system and the absolute (orbital) stability in the original system are examined. For the boundary exponential solutions corresponding to infection-free or totally infected status, we formulate the stability condition using reproduction numbers. We show that bi-unstability of boundary exponential solutions is one of conditions which guarantee the existence of coexistent exponential solutions.