具有耐药性的HIV模型研究

Study on HIV Model with Drug Resistance

HIV对药物抑制作用和长期服用药物的不依从性导致具有耐药性的HIV疾病的发病率不断提高.根据HIV传播的特点,建立具有敏感性和耐药性的感染初期、潜伏期和艾滋病前期的数学模型.研究模型的非负和有界性,并运用基本再生矩阵、谱半径和Lyapunov-Lasalle定理讨论模型的无病平衡点、边界平衡点、地方病平衡点的存在性和稳定性的充分条件.结果表明:改变参数数值可以控制传染病的蔓延,并通过数值模拟验证结论.

Inhibition to the drug and noncompliance with long-term use of drugs lead to an increased incidence of HIV disease with drug resistance.According to the dissemination characteristics of HIV,a mathematical model was established for the early stages of infection with sensitivity and drug,the incubation period and pre AIDS.The non-negativity and boundless of the model are researched.By using the basic regeneration matrix,spectral radius and Lyapunov-Lasalle＇s theorem,the sufficient conditions for the existence and stability of disease-free equilibrium point,boundary equilibrium point,and endemic equilibrium point of the model are discussed.The results show that changing the parameter values can control the spread of infectious diseases,and the conclusion is verified through numerical simulation.