具有加强诊断措施的Filippov HIV/AIDS传染病模型

A Filippov HIV/AIDS Epidemic Model Describing the Enhanced Diagnosis Measure Effect

本文建立Filippov HIV/AIDS传染病模型,用以刻画如下诊断措施:一旦已诊断HIV感染者数量超过某一水平,便启用加强的诊断措施;否则实施普通的诊断措施.应用等效控制法讨论了所建立模型的滑动模式区域和滑动动力学,在此基础上通过定性分析讨论了模型的全局动力学.数值结果表明,当阈值水平足够高或足够低时,HIV感染者数量最终稳定在一个相对较高或较低的水平;若选取一个恰当的阈值,HIV感染者数量最终会围绕该阈值波动.这说明阈值水平的选取对控制HIV至关重要,据此可确定是否有必要实施加强的诊断措施.

A Filippov system has been proposed to describe the following diagnosis measure in HIV control:once the number of the diagnosed HIV infected individuals is above a certain level,the enhanced diagnosis measure is carried out;otherwise,a general diagnosis ratio is adopted.The sliding mode region and the sliding mode dynamics are explored by using equivalent control method.We also examine the global dynamics of the model based on the sliding mode dynamics and qualitative analysis.The main results show that the number of HIV infected cases can stabilize at a relatively high level or relatively low level if the threshold value is enough high or enough low.By choosing an appropriate threshold value,the number of HIV infected individuals fluctuates around this threshold level.Therefore,it is important to choose a threshold value properly for HIV control,according to which one can determine whether or not it is necessary to implement the enhanced diagnosis measure.