Li Zhiming, Teng Zhidong, Miao Hui
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, China.
College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi, China.
Comput Math Methods Med. 2017;2017:8935314. doi: 10.1155/2017/8935314. Epub 2017 Sep 12.
HIV is one of the major life-threatening viruses that are spreading in the People's Republic of China (China for short). A susceptible-exposed in the latent stage-infectious (SEI) model is established to sketch the evolution of epidemic. The basic reproduction number is defined. By constructing Lyapunov function, globally asymptotical stabilities of the disease-free and endemic equilibria are given. Then, optimal control theory is applied in HIV/AIDS epidemic. Precaution, screening, and treatment of control variables are introduced and a new model with control is established. Through the HIV/AIDS data in China, all parameters involved in SEI model are analyzed and parts of them are estimated. Further, by control model, optimal strategy is obtained. Results show that the precaution and treatment are the major contributors to preventing and controlling HIV/AIDS epidemic.
艾滋病病毒是在中国（以下简称中国）传播的主要威胁生命的病毒之一。建立了一个易感染-暴露于潜伏期-感染期（SEI）模型来描绘疫情的演变。定义了基本再生数。通过构造李雅普诺夫函数，给出了无病平衡点和地方病平衡点的全局渐近稳定性。然后，将最优控制理论应用于艾滋病疫情。引入了控制变量的预防、筛查和治疗，并建立了一个带控制的新模型。通过中国的艾滋病数据，对SEI模型中涉及的所有参数进行了分析，并对其中部分参数进行了估计。此外，通过控制模型，获得了最优策略。结果表明，预防和治疗是预防和控制艾滋病疫情的主要因素。
