复杂网络上具有疫苗接种的传染病传播动力学分析

Dynamics analysis of infectious diseases transmission with vaccination on complex networks

摘要

基于复杂网络建立具有不同传染性的无症状感染者 A 与染病者 I 且具有疫苗接种的 SVAIR 传染病模型。利用下一代矩阵法求得基本再生数 R₀。并利用 Lyapunov 函数方法和单调迭代方法证明:当 R₀<1 时,无病平衡点是全局渐近稳定的;当 R₀>1时,地方病平衡点存在惟一性,系统一致持续且地方病平衡点是全局吸引的。最后,选择无标度网络进行敏感性分析和数值模拟,验证理论结果,结果显示,提高疫苗效力和疫苗接种率可以更好地控制传染病的传播。

Abstract

In this paper, based on complex networks, an SVAIR epidemic model with vaccination is established, in which the asymptomatic infected person (A) and the infected person (I) have different infectivity. The basic reproduction number R₀ is calculated by the next generation matrix. By using the Lyapunov function and monotone iterative, it is proved that when R₀<1, the disease-free equilibrium is globally asymptotically stable. When R₀ > 1, the endemic equilibrium point exists and is unique, the system is uniformly persistent and the endemic equilibrium point is globally attractive. Finally, we choose the scale-free network for sensitivity analysis and numerical simulation to verify the theoretical results, and results indicate that improving vaccine efficacy and vaccination rate can better control the spread of infectious diseases.

关键词

疫苗接种 / 无症状感染者 / 稳定性 / 复杂网络

Key words

vaccination / asymptomatic patient / stability / complex networks

参考文献

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基金资助

国家自然科学基金项目(12001501)

国家自然科学基金项目(12071445)

国家自然科学基金项目(11571324)

国家自然科学基金项目(12101574)

山西省自然科学基金项目(20210302124621)