In this research article, the authors intend to develop and analyze an epidemic model that describes the progression of acute and chronic HBV in a population. The threshold number ${\mathcal{R}}_0$ was obtained using the well-known next-generation matrix approach. The stability of disease-free and disease present states of the proposed model is investigated using the basic reproduction number. Results found during dynamical analysis show that the model exhibits backward bifurcation. To control the spread of infection; vaccination and treatment were introduced as control variables in the model. The key strategy is to decrease the number of acute and chronic infected people with the lowest possible cost. To support the theoretical results, sample simulations were presented at the end of the work.

在这篇研究文章中，作者打算开发和分析一种流行模型，该模型描述了人群中急性和慢性HBV的进程。门槛数${\mathcal{[R}}_0$使用众所周知的下一代矩阵方法获得。使用基本繁殖数研究所提出模型的无病状态和疾病当前状态的稳定性。动力学分析过程中发现的结果表明该模型表现出向后的分叉。控制感染的传播；在模型中引入了疫苗接种和治疗作为控制变量。关键策略是以最低的成本减少急慢性感染者的数量。为了支持理论结果，在工作结束时提供了样本模拟。