We formulate and systematically study a deterministic compartmental model of Hepatitis B. This model has some important and novel features compared with the well-known basic model in the literature. Specifically, it takes into account the differential susceptibility that follows the vaccine formulation employing three-doses schedule. It points up the HbeAg status of carriers, their levels of viral replication, the fact that treatment being not curative is recommended only to a small proportion of chronic carriers, and finally the fact that only inactive carriers are able to recover from disease. The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number [Formula: see text] and an endemic equilibrium when [Formula: see text]. By the use of Lyapunov functions, when it exists, we prove the global asymptotic stability of the endemic equilibrium under some conditions. Using data from Tokombere, a rural area in Cameroon, numerical simulations are performed. These numerical simulations first confirm analytical results, second they suggest that a policy based on treatment could not significantly impact the course of the infection. Third, they show as it is well known that vaccination is a very effective measure to control the infection. Furthermore, they show that neonatal vaccination influences more the course of infection than mass vaccination strategy. Nevertheless, they picture how much loss between consecutive doses of vaccine could be harmful. Finally, it is suggested that for a Sub-saharan African rural area, two-thirds of expected incidence of Hepatitis B virus infection and one third of expected prevalence of chronic carriers could be averted by 2030 if the birth dose vaccination becomes systematic and if mass vaccination rate increases to up 10%.

中文翻译：

---

撒哈拉以南非洲农村地区乙型肝炎病毒感染模型的全球动态

我们制定并系统地研究了乙型肝炎的确定性隔室模型。与文献中众所周知的基本模型相比，该模型具有一些重要和新颖的特征。具体来说，它考虑了采用三剂计划的疫苗制剂后的不同敏感性。它指出了携带者的 HbeAg 状态、他们的病毒复制水平、仅向一小部分慢性携带者推荐治疗无效的事实，最后指出只有非活动携带者能够从疾病中恢复的事实。该模型具有简单的动力学行为，当基本繁殖数[公式：参见文本]时具有全局渐近稳定的无病平衡，当[公式：参见文本]时具有地方性平衡。利用李雅普诺夫函数，当它存在时，我们证明了地方性平衡在某些条件下的全局渐近稳定性。使用来自喀麦隆农村地区 Tokombere 的数据，进行了数值模拟。这些数值模拟首先证实了分析结果，其次它们表明基于治疗的政策不会显着影响感染过程。第三，众所周知，疫苗接种是控制感染的非常有效的措施。此外，他们表明新生儿疫苗接种对感染过程的影响大于大规模疫苗接种策略。然而，他们描绘了连续接种疫苗之间的损失有多少可能是有害的。最后，建议对于撒哈拉以南非洲农村地区，