Chekroun Abdennasser, Frioui Mohammed Nor, Kuniya Toshikazu, Touaoula Tarik Mohammed
Laboratoire d'Analyse Nonlinéaire et Mathématiques Appliquées, University of Tlemcen, Tlemcen 13000, Algeria.
Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.
Math Biosci Eng. 2019 Feb 26;16(3):1525-1553. doi: 10.3934/mbe.2019073.
In this paper, we focus on the study of the dynamics of a certain age structured epidemic model. Our aim is to investigate the proposed model, which is based on the classical SIR epidemic model, with a general class of nonlinear incidence rate with some other generalization. We are interested to the asymptotic behavior of the system. For this, we have introduced the basic reproduction number R₀ of model and we prove that this threshold shows completely the stability of each steady state. Our approach is the use of general constructed Lyapunov functional with some results on the persistence theory. The conclusion is that the system has a trivial disease-free equilibrium which is globally asymptotically stable for R₀ < 1 and that the system has only a unique positive endemic equilibrium which is globally asymptotically stable whenever R₀ > 1. Several numerical simulations are given to illustrate our results.
在本文中，我们专注于研究某一具有年龄结构的流行病模型的动力学。我们的目标是研究这个基于经典SIR流行病模型提出的模型，它具有一类一般的非线性发病率以及其他一些推广。我们关注该系统的渐近行为。为此，我们引入了模型的基本再生数(R_0)，并证明这个阈值完全显示了每个稳态的稳定性。我们的方法是使用一般构造的李雅普诺夫泛函以及一些关于持久性理论的结果。结论是，该系统有一个无病平凡平衡点，当(R_0 < 1)时它是全局渐近稳定的，并且当(R_0 > 1)时系统只有一个唯一的正地方病平衡点，它也是全局渐近稳定的。给出了几个数值模拟来说明我们的结果。
