An Jing, Hao Wenhui, Guo Huifen, Zhang Juping
Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi, 030006, China.
Shanxi Key Laboratory for Mathematical Technology in Complex Systems, Taiyuan, Shanxi, 030006, China.
Infect Dis Model. 2025 Aug 7;10(4):1533-1574. doi: 10.1016/j.idm.2025.08.001. eCollection 2025 Dec.
The dynamic system of HPV transmission with age subgroups, sexual and nonsexual transmission is established based on HPV vaccination. Firstly, the transmission threshold of the system is given. Local asymptotically stabilization of disease-free equilibrium when < 1 is proved. It is proved that there is a positive equilibrium and disease persistence in the system when > 1. Secondly, parameters estimation of the system is carried out based on the data from Chinese STD surveillance sites using the least square method. Finally, optimal control theory is applied to the system, the existence of optimal control is proved, and Pontryagin maximum principle is utilized to find optimal control strategy, and the spread of human papillomavirus in different age groups is predicted. The results show that for different age groups, vaccination of 16-45 years old is more beneficial to HPV control than vaccination of 9-15 years old, and that for different control costs, low-cost control is more advantageous.
基于人乳头瘤病毒（HPV）疫苗接种建立了具有年龄亚组、性传播和非性传播的HPV动态传播系统。首先，给出了该系统的传播阈值。证明了当<1时无病平衡点的局部渐近稳定性。证明了当>1时系统存在正平衡点且疾病持续存在。其次，利用最小二乘法根据中国性传播疾病监测点的数据对系统进行参数估计。最后，将最优控制理论应用于该系统，证明了最优控制的存在性，并利用庞特里亚金极大值原理找到最优控制策略，预测了人乳头瘤病毒在不同年龄组中的传播情况。结果表明，对于不同年龄组，16 - 45岁人群接种疫苗比9 - 15岁人群接种疫苗对HPV控制更有益，并且对于不同的控制成本，低成本控制更具优势。
