摘要
通过考虑同性接触与异性接触来研究HIV/AIDS的传播,建立带有性别结构的HIV/AIDS模型.根据下一代矩阵法求出基本再生数.证明当R_(0)<1时,无病平衡点是全局渐近稳定的,当R_(0)> 1时,地方病平衡点是存在的,并且疾病是一致持续的,并通过数值模拟来验证结论.提出一个最优控制问题并利用庞特里亚金极大值原理进行了求解.拟合结果表明我国未来几年患病人数仍会不断攀升.
Based on the fact that HIV/AIDS manifests different characteristics of transmission,we establish an HIV/AIDS epidemic model with sex structure which including homosexual contacts and heterosexual contacts.We derive the explicit expression for the basic reproduction number through the next generation matrix approach.If R_(0)<1,the diseasefree equilibrium is globally asymptotically stable.If R_(0)> 1,the model has an endemic equilibrium,and the disease is uniform persistence.In particular,numerical simulations are presented to reinforce these analytical results.We also formulate an optimal control problem and solve it using Pontryagins Maximum Principle.Data fitting indicates that the number of HIV/AIDS in China will continue to rise in the future years.
作者
杨雪
李淑萍
YANG Xue;LI Shu-ping(School of Science,North University ofChina,Taiyuan 030051,China)
出处
《数学的实践与认识》
2022年第11期159-171,共13页
Mathematics in Practice and Theory
基金
国家自然科学基金(12001501)
山西省青年基金(201901D211216)。
关键词
性别结构
稳定性
一致持续
敏感性分析
最优控制
sex structure
stability
uniform persistence
sensitivity analysis
optimal control
