复杂网络上具有阶段结构的乙肝传染病传播动力学分析及其最优控制

Dynamic Analysis and Optimal Control of Hepatitis B Virus Infectious Diseases Transmission with Stage-Structured on Complex Networks

摘要

首先,针对乙肝传播过程中染病者和病毒携带者具有不同传染力的特点,建立复杂网络上具有阶段结构的S_a^kS_n^kV_kE_kI_kC_kR_k传染病模型.其次,利用下一代矩阵法求得基本再生数R₀,结合矩阵理论和Lyapunov函数方法证明疾病平衡点的稳定性,并通过Pontryagin最大值原理讨论两种策略的最优控制问题.最后,基于无标度网络进行敏感性分析和数值模拟,以验证理论结果,并找到最优控制.结果表明,降低疫苗失效率和提高疫苗接种率都可以更好地控制传染病传播.

Abstract

Firstly,in view of characteristics of different infectivity of hepatitis B infectors and virus carriers in the process of hepatitis B transmission,we established an S_a^kS_n^kV_kE_kI_kC_kR_k epidemic model with stage-structured on complex networks.Secondly,we obtained the basic reproduction number R₀ by using the next generation matrix method,and combined the matrix theory and the Lyapunov function method to prove the stability of the disease equilibrium point.We also discussed the optimal control problems of two strategies by Pontryagin’s maximum principle.Finally,based on the scale-free network,the sensitivity analysis and numerical simulation were carried out to verify the theoretical results and find the optimal control.The results show that reducing vaccine inefficacy rate and increasing vaccination rate can better control the spread of infectious diseases.

关键词

复杂网络 / 乙肝病毒 / 疫苗接种 / 最优控制

Key words

complex network / hepatitis B virus / vaccination / optimal control

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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)

国家自然科学基金(11571324)

国家自然科学基金(12101574)

山西省自然科学基金(20210302124621)