一类具有控制措施的结核病治疗模型分析

Qualitative analysis of a class of tuberculosis model with drug resistance

以结核病的病理特征和传播机理为背景,建立和研究了一类具有优化控制措施的结核病动力学模型.对模型的基本再生数进行了敏感性分析;讨论了模型的非耐药和耐药的优化治疗控制措施,得到了使得目标函数取得最小值的最优控制对.最后,利用数值模拟展示了不同控制措施强度下的疾病传播情况.

In this paper,a tuberculosis transmission model with optimal control measures was established and studied based on the pathology and transmission mechanism of tuberculosis.We analysis the sensitivity of basic reproduction number,discuss the optimal control with non-drug resistance and drug resistance,and obtain the optimal control pairs which makes the objective function be the minimum value.At the end,the numerical simulation was used to show the transmission of tuberculosis under different control measures.