Dept. of Applied Mathematics, University of Malaga, Spain.
Math Biosci Eng. 2013 Aug;10(4):959-77. doi: 10.3934/mbe.2013.10.959.
In this work we propose the definition of the ratio of hidden infection of HIV/AIDS epidemics, as the division of the unknown infected population by the known one. The merit of the definition lies in allowing for an indirect estimation of the whole of the infected population. A dynamical model for the ratio is derived from a previous HIV/AIDS model, which was proposed for the Cuban case, where active search for infected individuals is carried out through a contact tracing program. The stability analysis proves that the model for the ratio possesses a single positive equilibrium, which turns out to be globally asymptotically stable. The sensitivity analysis provides an insight into the relative performance of various methods for detection of infected individuals. An exponential regression has been performed to fit the known infected population, owing to actual epidemiological data of HIV/AIDS epidemics in Cuba. The goodness of the obtained fit provides additional support to the proposed model.
在这项工作中，我们提出了 HIV/AIDS 流行中隐性感染比例的定义，即未知感染人群与已知感染人群的比值。该定义的优点在于允许对整个感染人群进行间接估计。从之前为古巴提出的 HIV/AIDS 模型中推导出了该比例的动力学模型，该模型通过接触者追踪计划对感染个体进行主动搜索。稳定性分析证明，该比例模型具有一个唯一的正平衡点，该平衡点是全局渐近稳定的。敏感性分析深入了解了检测感染个体的各种方法的相对性能。由于古巴 HIV/AIDS 流行的实际流行病学数据，我们已经进行了指数回归来拟合已知的感染人群。所得到的拟合效果良好，为所提出的模型提供了额外的支持。
