一类具有预防意识的多斑块SEIQR传染病模型的阈值动力学研究  

Threshold Dynamics of a Multi-Patch SEIQR Epidemic Model with Prevention Awareness

作　　者：沈鑫 刘子建 SHEN Xin;LIU Zijian(School of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)

机构地区：[1]重庆交通大学数学与统计学院,重庆400074

出　　处：《新疆大学学报（自然科学版中英文）》2024年第2期145-156,共12页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金“多干预脉冲动力学模型及药物毒理效应机制研究”(12271068);重庆市自然科学基金创新发展联合基金“肺癌细胞生理年龄分布的动力学研究”(CSTB2022NSCQ-LZX0026)。

摘　　要：结合一般传染病病毒传播的特点,提出了一类具有预防意识和斑块间流动感染的SEIQR传染病传播动力学模型.根据下一代矩阵法算出了单斑块下疾病传播的阈值R_(a)和两斑块下疾病传播的阈值R_(a)^(φ),得到当R_(a)≤1时单斑块下无病平衡点全局渐近稳定和R_(a)^(φ)≤1时两斑块下无病平衡点局部稳定的结论,数值模拟证实了理论结果.敏感性分析说明了参数对基本再生数的影响,结果表明增加人群预防意识能够抑制病毒在斑块间的传播,但群体在斑块间流动时发生感染会加剧病毒的传播.We consider the characteristics of viral transmission of common infectious diseases,multi-patch SEIQR infectious disease transmission dynamic model with prevention awareness was proposed and studied.According to the next generation matrix method,the disease transmission threshold R_(a) in a single patch and the disease transmission threshold R_(a)^(φ) in the two patches were calculated.The theoretical results show that the disease free equilibrium in a single patch is globally asymptotically stable if R_(a)≤1 and the disease free equilibrium in two patches are locally stable if R_(a)^(φ)≤1.Numerical simulations confirm the theoretical results,sensitivity analysis discusses the effects of parameters to the basic regeneration number,which shows that increasing the awareness of prevention could inhibit the spread of the virus between patches,but infection during transportation can increase it.

关 键 词：预防意识 斑块模型 无病平衡点 稳定性 

分 类 号：O175[理学—数学]