College of Science, Harbin University of Science and Technology, Harbin 150080, China.
Heilongjiang Hospital, Harbin 150036, China.
Math Biosci Eng. 2021 Sep 22;18(6):8257-8297. doi: 10.3934/mbe.2021410.
According to the mechanism of drug inhibition of hepatitis B virus and the analysis of clinical data, it is found that random factors in long-term treatment produced uncertainty and resistance to hepatitis B virus infection rate, a model of hepatitis B virus with random interference infection rate is established. By constructing Lyapunov function and using Ito's formula, it is proved that the stochastic hepatitis B model has a unique global positive solution. The sufficient conditions for the asymptotic behavior of solution are given. The relationship between noise intensity and oscillation amplitude is obtained. The effects of noise intensity on the asymptotic behavior of the model and antiviral therapy are simulated, and the conclusion of the theorem is verified. An interesting phenomenon is also found that with the increase of noise intensity, the number of drug-resistant viruses will decrease, which will affect the accuracy of a single test of HBV DNA. Therefore, it is suggested to increase the frequency and interval of tests.
根据药物抑制乙型肝炎病毒的作用机制和临床数据分析，发现长期治疗中的随机因素产生了乙型肝炎病毒感染率的不确定性和耐药性，建立了乙型肝炎病毒的随机干扰感染率模型。通过构建李雅普诺夫函数并使用伊藤公式，证明了随机乙型肝炎模型具有唯一的全局正解。给出了解的渐近行为的充分条件。得到了噪声强度与振幅度之间的关系。模拟了噪声强度对模型和抗病毒治疗的渐近行为的影响，并验证了定理的结论。还发现了一个有趣的现象，即随着噪声强度的增加，耐药病毒的数量将会减少，这将影响 HBV DNA 单次检测的准确性。因此，建议增加检测的频率和间隔。
