摘要
针对筛查和药物治疗对染病者传染性产生的影响,本文考虑了具有两种不同传染水平染病者的仓室数学模型.分析了模型平衡点的稳定性态,结果表明,当基本再生数小于1时,模型的无病平衡点全局稳定;当基本再生数大于1时,地方病平衡点在一定条件下也是全局稳定的.同时利用控制理论本文也研究了药物治疗的实施对染病者进行干预和影响的最优控制措施,寻找到了使目标函数值最小的治疗控制方法,并用数值模拟显示了模型解的动力学性态及治疗措施对防止疾病蔓延所起的作用.
In view of the impact of screening and treatment on patient’s infectivity, an epidemic model with two different infectivity has been studied, in which the stabilities are analyzed. It is proved that the disease-free equilibrium is globally stable when the basic reproductive number is less than one, and when it is greater than one, the endemic equilibrium is also globally stable under certain conditions. The impact of treatment on the infections is also formulated and solved as an optimal control problem. The optimal solution of the model is found which can make the minimum value of the objective function, and the numerical results show the dynamics of the solutions and the performance of the optimization strategy.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2014年第1期1-10,共10页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金(11101330)
陕西省科技新星计划(2013KJXX-34)
陕西省教育厅基金(2013JK0582)
西安市科技局项目(CXY1341(4))
关键词
流行病
治疗措施
数学模型
稳定性
最优控制
epidemic
treatment
mathematical model
stability
optimal control
