基于信息干预下HBV传染病模型稳定性分析与最优控制  

Stability Analysis and Optimal Control of HBV Epidemic Model Based on Information Intervention

作　　者：张靖文 王浩华 Zhang Jingwen;Wang Haohua(School of Sciences,Hainan University,Haikou 570228,China;Hainan Key Laboratory for Engineering Modeling and Statistical Calculation,Haikou 570228,China;Ministry of Education Key Laboratory for Genetics&Germplasm Enhancement of Tropical Specialty Forest and Flowers and Plants,Haikou 570228,China)

机构地区：[1]海南大学理学院,海南海口570228 [2]海南大学海南省工程建模与统计计算重点实验室,海南海口570228 [3]海南大学热带特色林木花卉遗传与种质创新教育部重点实验室,海南海口570228

出　　处：《海南大学学报（自然科学版）》2022年第1期39-49,共11页Natural Science Journal of Hainan University

基　　金：国家自然科学基金(11761025,11961018);海南省自然科学基金(120RC451);海南省研究生创海南省研究生创新科研课题(Hys2020-108,Qhys2021-208)。

摘　　要：构建了基于信息干预下的HBV传染病模型,揭示疫苗接种以及信息宣传对其传播动力学的影响.首先,通过计算模型的基本再生数和2个平衡点,给出了模型渐进稳定性的充分条件,并对参数进行了局部敏感性分析,考察其分支性质;其次,选择疫苗有效率、信息反应强度以及有效治疗率作为控制变量,探究最优控制下HBV传播动力学;最后,数值模拟验证了平稳性条件:基本再生数R_(0)>1时模型有全局渐近稳定的疾病平衡点,R0<1时模型有全局渐近稳定的无病平衡点.模型对比结果表明,最优三维控制模型不仅能大幅度地降低感人数,避免峰值出现,还能有效缩短病源的阻断时间,使恢复人群在短时间内达到峰值.In the report,an HBV infectious disease model based on information intervention was constructed,by which the effects of the vaccination and information propaganda on its transmission dynamics were analyzed.Firstly,the basic regeneration number and two equilibrium points of the model were calculated,the sufficient conditions for the asymptotic stability of the model were obtained,the branching properties were investigated,and the local sensitivity analysis of the parameters was performed;Secondly,the effective rate of vaccine,the information response intensity,and the effective treatment rate were used as the control variables to explore the dynamics of HBV transmission under optimal control;Finally,the numerical simulation verified the stability conditions,when the basic regeneration number(R_(0))was above 1,the model has a globally asymptotically stable disease equilibrium,when R;is less than 1,the model has a globally asymptotically stable disease-free equilibrium.The model comparison results showed that the optimal three-dimensional control model can not only greatly reduce the number of people infected and avoid peaks,but also effectively shorten the blocking time of the source of the disease,and the recovery population can reach the peak in a short time.

关 键 词：传染病模型 信息干预 局部敏感性分析 最优控制 数值模拟 

分 类 号：R181[医药卫生—流行病学] O232[医药卫生—公共卫生与预防医学]