入射(几何)
数学
基本再生数
理论(学习稳定性)
非线性系统
稳定性理论
李雅普诺夫函数
群(周期表)
应用数学
流行病模型
接种疫苗
纯数学
计算机科学
人口学
物理
医学
几何学
病毒学
社会学
机器学习
量子力学
人口
出处
期刊:Discrete and Continuous Dynamical Systems-series B
[American Institute of Mathematical Sciences]
日期:2016-01-01
卷期号:21 (3): 977-996
被引量:15
标识
DOI:10.3934/dcdsb.2016.21.977
摘要
A multi-group epidemic model with general nonlinear incidence and vaccination age structure has been formulated and studied. Mathematical analysis shows that the global stability of disease-free equilibrium and endemic equilibrium of the model are determined by the basic reproduction number $\mathcal{R}_0$: the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_01$. The Lyapunov functionals for the global dynamics of the multi-group model are constructed by applying the theory of non-negative matrices and a novel grouping technique in estimating the derivative.
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