乙肝病毒的数学模型及定性分析
发布时间：2018-10-29 16:07
【摘要】：本文主要讨论了三类乙肝病毒数学模型，得到了平衡点稳定性的充分条件。 首先，基于Nowak模型，建立了具免疫时滞因素HBV感染时滞微分方程模型,得到了基本再生数，并应用Routh-Hurwitze定理及Lyapunov-Lasalle定理讨论了该模型正平衡点的稳定性,分析了免疫时滞对系统动力学性质产生的影响。数值模拟验证了所得到的结果。 其次，在模型的基础上，以Revilla模型（1）及Levins模型（2）为基础所建立一个考虑药物治疗引起免疫应答的四个态变量的数学模型，该模型对慢性HBV感染的药物的长期治疗效果进行了预测。数值模拟结果表明：在使用药物3个月后，，病毒数量几乎稳定，存在平衡状态。当满足一定条件时，延长治疗患病者时间。则患病者体内的HBV很有可能完全被清除。若我们所选取的参数不同时，治疗的结果可能有很大的差异性。 最后，建立了微分方程预防接种乙型肝炎数学模型。应用Routh-Hurwitze定理，证明了该传染病模型平衡点是渐近稳定的。建议采取新生婴儿免疫接种的控制方法是预防乙肝病毒传染的重要策略。
[Abstract]:In this paper, three kinds of mathematical models of hepatitis B virus are discussed, and sufficient conditions for the stability of the equilibrium point are obtained. Firstly, based on the Nowak model, the differential equation model of HBV infection delay with immune delay factor is established, and the basic reproducing number is obtained. The stability of the positive equilibrium point of the model is discussed by using Routh-Hurwitze theorem and Lyapunov-Lasalle theorem. The effect of immune delay on the dynamic properties of the system is analyzed. The results obtained are verified by numerical simulation. Secondly, on the basis of Revilla model (1) and Levins model (2), a mathematical model considering the four state variables of immune response induced by drug therapy was established. The model predicts the long-term efficacy of drugs for chronic HBV infection. The results of numerical simulation show that after 3 months of drug use, the virus quantity is almost stable and in equilibrium state. When certain conditions are met, the duration of treatment is prolonged. The HBV in the patient is likely to be completely eliminated. If the parameters we selected are different, the outcome of the treatment may be very different. Finally, a mathematical model of differential equation vaccination for hepatitis B was established. By using Routh-Hurwitze theorem, it is proved that the equilibrium point of the epidemic model is asymptotically stable. It is suggested that the control method of infant immunization is an important strategy to prevent hepatitis B virus infection.
【学位授予单位】：南华大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O175
本文编号：2298164
[Abstract]:In this paper, three kinds of mathematical models of hepatitis B virus are discussed, and sufficient conditions for the stability of the equilibrium point are obtained. Firstly, based on the Nowak model, the differential equation model of HBV infection delay with immune delay factor is established, and the basic reproducing number is obtained. The stability of the positive equilibrium point of the model is discussed by using Routh-Hurwitze theorem and Lyapunov-Lasalle theorem. The effect of immune delay on the dynamic properties of the system is analyzed. The results obtained are verified by numerical simulation. Secondly, on the basis of Revilla model (1) and Levins model (2), a mathematical model considering the four state variables of immune response induced by drug therapy was established. The model predicts the long-term efficacy of drugs for chronic HBV infection. The results of numerical simulation show that after 3 months of drug use, the virus quantity is almost stable and in equilibrium state. When certain conditions are met, the duration of treatment is prolonged. The HBV in the patient is likely to be completely eliminated. If the parameters we selected are different, the outcome of the treatment may be very different. Finally, a mathematical model of differential equation vaccination for hepatitis B was established. By using Routh-Hurwitze theorem, it is proved that the equilibrium point of the epidemic model is asymptotically stable. It is suggested that the control method of infant immunization is an important strategy to prevent hepatitis B virus infection.
【学位授予单位】：南华大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O175
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