Zhang Tai Lei, Li Hui, Xie Na, Fu Wen Hui, Wang Kai, Ding Xiong Jie
School of Science, Chang'an University, Xi'an, 710064, China.
Central Laboratory of Xinjiang Medical University, Urumqi, China.
Math Biosci Eng. 2019 Dec 13;17(2):1757-1775. doi: 10.3934/mbe.2020092.
The incubation period for Hepatitis B virus (HBV) within the human is epidemiologically significant because it is typically of long duration (1.5∼6 months) and the disease transmission possibility may be increased due to more contact from the patients in this period. In this paper, we investigate an SEICRV epidemic model with time delay to research the transmission dynamics of Hepatitis B disease. The basic reproductive number ${\mathcal R}_0$ is derived and can determine the dynamics of the model. The disease-free equilibrium is globally asymptotically stable if ${\mathcal R}_0<1 and="" unstable="" if="" mathcal="" r="" _0="">1$. As ${\mathcal R}_0>1$, the model admits a unique endemic equilibrium which is locally asymptotically stable. The endemic equilibrium is globally asymptotically stable when the vertical transmission is ignored. Numerically, we study the Hepatitis B transmission case in Xinjiang, China. Using the Hepatitis B data from Xinjiang, the basic reproductive number is estimated as 1.47 (95% CI: 1.34-1.50). By the end of 2028, the cumulative number of Hepatitis B cases in Xinjiang will be estimated about 700,000 if there is no more effective preventive measures. The sensitivity analysis of ${\mathcal R}_0$ in terms of parameters indicates prevention and treatment for chronic patients are key measures in controlling the spread of Hepatitis B in Xinjiang.
乙肝病毒（HBV）在人体内的潜伏期具有重要的流行病学意义，因为其潜伏期通常较长（1.5至6个月），且在此期间患者接触增多可能会增加疾病传播的可能性。在本文中，我们研究一个具有时滞的SEICRV传染病模型，以探讨乙肝疾病的传播动力学。推导了基本再生数${\mathcal R}_0$，它可以确定模型的动态特性。当${\mathcal R}_0<1$时，无病平衡点是全局渐近稳定的；当${\mathcal R}_0>1$时，无病平衡点是不稳定的。当${\mathcal R}_0>1$时，模型存在唯一的地方病平衡点，该平衡点是局部渐近稳定的。当忽略垂直传播时，地方病平衡点是全局渐近稳定的。在数值上，我们研究了中国新疆的乙肝传播情况。利用新疆的乙肝数据，估计基本再生数为1.47（95%置信区间：1.34 - 1.50）。如果没有更有效的预防措施，到2028年底，新疆乙肝病例的累计数量预计约为70万。对${\mathcal R}_0$关于参数的敏感性分析表明，对慢性病患者的预防和治疗是控制新疆乙肝传播的关键措施。
