复杂网络上考虑疫苗接种和失效的疟疾传播动力学分析

Malaria transmission dynamics on complex networks with vaccination and failure

摘要

本文基于复杂网络建立了具有疫苗接种和失效的疟疾传播动力学模型,首先利用正平衡点的存在性计算了基本再生数R₀,然后证明了当R₀<1时无病平衡点的局部渐近稳定性和全局渐近稳定性,同时证明了当R₀>1时系统是一致持续的;最后,进行了敏感性分析和数值模拟验证了理论结果.

Abstract

In this paper, we established a model of malaria transmission dynamics with vaccination and failure based on complex networks. Firstly, we calculated the basic reproduction number R ₀ using the existence of positive equilibrium point. Then we proved the local asymptotic stability and global asymptotic stability of disease-free equilibrium point when R ₀<1 and meanwhile we proved that the system is uniformly persistent when R ₀>1. Lastly, we carried out the sensitivity analyses and numerical simulations to validate the theoretical results.

关键词

疟疾 / 疫苗接种 / 稳定性 / 复杂网络

Key words

malaria / vaccination / stability / complex networks

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基金资助

国家自然科学基金(12001501)

国家自然科学基金(12071445)

山西省自然科学基金(20210302124621)