| 具有两个感染阶段和治疗及非线性发生率的HIV/AIDS模型的研究 |
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| 引用本文： | 王非,杨亚莉,金英姬,曹书苗.具有两个感染阶段和治疗及非线性发生率的HIV/AIDS模型的研究[J].山东大学学报(理学版),2019,54(10):67-73. |
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| 作者姓名： | 王非 杨亚莉 金英姬 曹书苗 |
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| 作者单位： | 1.空军工程大学基础部应用数学与军事密码教研室, 陕西 西安 710051;2.西藏民族大学教育学院, 陕西 咸阳 712082;3.西安建筑科技大学, 教育部西北水资源与生态环境重点实验室, 陕西 西安 710055 |
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| 基金项目： | 国家自然科学基金资助项目(11661073);西藏自治区自然科学基金资助项目(2016ZR-15-19) |
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| 摘 要： | 基于HIV/AIDS的实际传播状况及治疗情况,建立了具有两个感染阶段和治疗的非线性发生率HIV/AIDS传染病数学模型。首先利用极限理论讨论了系统可行域的范围;其次通过构造再生矩阵得到基本再生数;然后对基本再生数的范围展开讨论,给出了平衡点的存在情况及个数;最后通过构造Lyapunov函数、利用Lasalle不变集、布森伯格定理和范登德莱西原理等证明了无病平衡点、地方病平衡点的局部性态和全局性态,并给出了数值模拟的结果。
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| 关 键 词： | HIV/AIDS 非线性发生率 基本再生数 LaSalle不变集原理 Lyapunov函数 |
Study on nonlinear HIV/AIDS model with two infection stages treatment and incidence rate |
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| WANG Fei,YANG Ya-li,JIN Ying-ji,CAO Shu-miao.Study on nonlinear HIV/AIDS model with two infection stages treatment and incidence rate[J].Journal of Shandong University,2019,54(10):67-73. |
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| Authors: | WANG Fei YANG Ya-li JIN Ying-ji CAO Shu-miao |
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| Institution: | 1. Department of Applied Mathematics and Military Cryptography, Air Force Engineering University, Xian 710051, Shaanxi, China;2. College of Education, Tibetan University for Nationalities, Xianyang 712082, Shaanxi, China;3. Xian University of Architecture and Technology, Shaanxi Key Laboratory of Environmental Engineering, School of Environmental and Municipal Engineering, Xian 710055, Shaanxi, China |
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| Abstract: | Based on the actual transmission and treatment, a mathematical model of HIV/AIDS with two infection stages, treatment and non-linear incidence is established in this paper.Then the range of the feasible region of the system is discussed by using the limit theory.Secondly, the basic regeneration number is obtained by constructing regeneration matrix, and the range of the basic regeneration number is discussed. The existence and number of equilibrium points are obtained.Finally, the local and global properties of equilibrium point are proved by constructing Lyapunov function, using Lasalle invariant set, Boosenberg theorem and Van den Lacy principle. |
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| Keywords: | HIV/AIDS nonlinear incidence basic regeneration number LaSalle invariant set principle Lyapunov function |
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