具有主动免疫与药物治疗控制乙肝病毒传播的动力学模型

发布时间：2018-08-09 17:16

【摘要】：乙型肝炎(简称“乙肝”)是由乙型肝炎病毒引起的一种传染病。通常人们采取主动免疫(接种疫苗)预防乙肝病毒的感染,采取药物治疗抑制乙肝病毒感染者体内病毒复制,从而控制乙肝的传播。本文主要研究工作如下:考虑临床上治疗疾病的需要,建立了多次给药的药物动力学模型来分析用药方案。给出了不同药物剂量在两种给药方式下的血药浓度-时间关系式。将模型的研究结果应用到早产儿呼吸暂停治疗案例中,以安全、不浪费且能够维持稳定药效为准则,分析给药方案的可行性。并且针对病情严重患儿的治疗,设计了个性化给药方案。考虑到乙肝病毒感染者主要来源于新生儿、免疫失效者,建立了具有主动免疫控制乙肝病毒传播的SEICR模型。利用微分方程理论,给出了无病平衡点和地方病平衡点存在性与全局渐近稳定性的充分条件。运用数值模拟验证了结果的合理性。接种疫苗比例的变化会改变垂直感染率和易感者与病毒感染者之间的有效接触率,再通过MATLAB数值模拟接种疫苗比例、垂直感染率和有效接触率对乙肝病毒携带者的影响。数值模拟结果显示,主动免疫可以有效地控制乙肝病毒的传播。考虑到药物治疗对乙肝病毒感染者控制的作用,在治疗期间将乙肝病毒感染者药物治疗比例视为时间的函数,给出了具有药物治疗的乙肝病毒传播动力学模型。在此基础上,以减少乙肝病毒感染者数量为目的,建立了乙肝病毒感染者与药物治疗比例的目标函数。运用最优控制存在的充分条件,证明了最优治疗比例的存在性。且利用Pontryagin极大值原理,找到最优药物治疗比例表达式。通过数值模拟验证结果的可行性,结合实际数据分析发现,当选取最优药物治疗比例时,乙肝病毒感染者在20年内降低到1%。
[Abstract]:Hepatitis B is an infectious disease caused by hepatitis B virus. Usually people take active immunization (vaccination) to prevent hepatitis B virus infection, take drug treatment to inhibit virus replication in the body of hepatitis B virus infection, so as to control the spread of hepatitis B. The main work of this paper is as follows: considering the need of clinical treatment, a pharmacokinetic model was established to analyze the drug regimen. The relationship between plasma concentration and time of different drug doses was given. The results of the model were applied to the apnea treatment of premature infants. The feasibility of drug administration was analyzed based on the criteria of safety, no waste and the ability to maintain stable efficacy. And for the treatment of children with severe illness, a personalized drug delivery scheme was designed. Considering that hepatitis B virus infection mainly comes from newborns and immune failure, a SEICR model with active immunity to control the transmission of hepatitis B virus is established. By using the theory of differential equations, sufficient conditions for the existence and global asymptotic stability of disease-free and endemic equilibrium points are given. The rationality of the results is verified by numerical simulation. The proportion of vaccinated vaccine will change the vertical infection rate and the effective contact rate between the susceptible person and the virus infected person. Then the effect of inoculation proportion vertical infection rate and effective contact rate on HBV carriers is simulated by MATLAB numerical simulation. Numerical simulation results show that active immunization can effectively control the spread of hepatitis B virus. Considering the effect of drug therapy on the control of hepatitis B virus infection, a dynamic model of hepatitis B virus transmission with drug therapy was given, in which the proportion of drug treatment was regarded as a function of time. On this basis, the objective function of the proportion of hepatitis B virus infection and drug therapy was established in order to reduce the number of hepatitis B virus infected persons. The existence of optimal treatment proportion is proved by using the sufficient condition of optimal control. Based on the principle of Pontryagin Maxima, the optimal proportion expression of drug therapy was found. The feasibility of the results was verified by numerical simulation. It was found that when the optimal proportion of drug treatment was selected, the hepatitis B virus infection rate decreased to 1 in 20 years.
【学位授予单位】：哈尔滨理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：R512.62

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