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基于疫苗接种的SEIHRVI传染病模型分析与最优控制

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为研究疫苗接种对控制传染病的影响,建立了具有标准发生率的传染病模型.通过推导得出模型的基本再生数,给出地方病平衡点的存在条件.借助构造Lyapunov函数证明了平衡点的全局稳定性.应用Pontryagin最大值原理分析了最优控制问题,得出最优控制策略.结果表明:提高疫苗接种率和效力能有效控制疾病传播;注意自我保护,及时接种以及重视治疗一定程度上可减小疾病爆发的规模.
Analysis and Optimal Control of an SEIHRVI Epidemic Model Based on Vaccination
In order to study the effect of vaccination on the control of infectious diseases,an epidemic model with standard incidence rate was developed.The basic reproduction number of the model was derived and the condition for the existence of the endemic equilibrium was given.By constructing Lyapunov function,the global stability of equilibrium was proved.Pontryagin's maximum principle was applied to analyze the optimal control problem and the optimal control strategy was obtained.The results showed that improving the vaccination rate and vaccine efficacy could effectively control the spread of the disease.Paying attention to self-protection,timely vaccination,and treatment could reduce the scale of disease outbreaks to a certain extent.

stability theoryvaccinationepidemic modeloptimum controlnumerical simulation

薛亚奎、任亚鑫

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中北大学 数学学院,山西太原 030051

齐鲁理工学院 计算机与信息工程学院,山东济南 250200

稳定性理论 疫苗接种 传染病模型 最优控制 数值模拟

国家自然科学基金资助项目山西省自然科学青年基金资助项目

11971278201801D221040

2024

沈阳大学学报(自然科学版)
沈阳大学

沈阳大学学报(自然科学版)

CSTPCD
影响因子:0.475
ISSN:2095-5456
年,卷(期):2024.36(1)
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