【摘要】：本文主要討論了三類乙肝病毒數(shù)學(xué)模型，得到了平衡點(diǎn)穩(wěn)定性的充分條件。 首先，基于Nowak模型，建立了具免疫時(shí)滯因素HBV感染時(shí)滯微分方程模型,得到了基本再生數(shù)，并應(yīng)用Routh-Hurwitze定理及Lyapunov-Lasalle定理討論了該模型正平衡點(diǎn)的穩(wěn)定性,分析了免疫時(shí)滯對(duì)系統(tǒng)動(dòng)力學(xué)性質(zhì)產(chǎn)生的影響。數(shù)值模擬驗(yàn)證了所得到的結(jié)果。 其次，在模型的基礎(chǔ)上，以Revilla模型（1）及Levins模型（2）為基礎(chǔ)所建立一個(gè)考慮藥物治療引起免疫應(yīng)答的四個(gè)態(tài)變量的數(shù)學(xué)模型，該模型對(duì)慢性HBV感染的藥物的長期治療效果進(jìn)行了預(yù)測(cè)。數(shù)值模擬結(jié)果表明：在使用藥物3個(gè)月后，，病毒數(shù)量幾乎穩(wěn)定，存在平衡狀態(tài)。當(dāng)滿足一定條件時(shí)，延長治療患病者時(shí)間。則患病者體內(nèi)的HBV很有可能完全被清除。若我們所選取的參數(shù)不同時(shí)，治療的結(jié)果可能有很大的差異性。 最后，建立了微分方程預(yù)防接種乙型肝炎數(shù)學(xué)模型。應(yīng)用Routh-Hurwitze定理，證明了該傳染病模型平衡點(diǎn)是漸近穩(wěn)定的。建議采取新生嬰兒免疫接種的控制方法是預(yù)防乙肝病毒傳染的重要策略。
[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.
【學(xué)位授予單位】：南華大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：O175

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