This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20–43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919–2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. It is concluded that joint implementation of these measures can minimize the numbers of exposed and infectious individuals in the shortest time, so it is the most efficient strategy to curb the hepatitis B epidemic. Moreover, vaccination for newborns plays the core role and maintains the high level of population immunity.

这项工作将 Lu 和 Lu (NARWA 36:20–43, 2017) 开发的非线性自主微分方程的新几何标准应用于具有临时免疫的非线性 SEIVS 流行病模型，并实现了其阈值动力学。具体来说，Cai 和 Li 的 SEIVS 模型 (AMM 33:2919–2926, 2009) 的全局稳定性问题得到了有效解决。进一步建立了相应的疫苗接种、宣传活动和治疗的最佳控制体系，并通过数值模拟比较了四种不同的控制策略来遏制乙型肝炎。得出的结论是，这些措施的联合实施可以最大限度地减少乙型肝炎的暴露和感染人数。时间最短，是遏制乙肝疫情最有效的策略。而且，