Abstract：
COVID-19 vaccines have been illustrated to lessen the growth of sickness caused by the virus effectively. In any case, inoculation has consistently been controversial, with differing opinions and viewpoints. This has compelled some individuals to decide against receiving the vaccine. These divergent viewpoints have had a trivial impact on the epidemic\'s dynamics and the disease\'s development. In response to vaccinated individuals still falling ill, many countries have implemented booster vaccines to protect further. In this specific investigation, a mathematical model composed of seven compartments is employed to examine the effectiveness of a booster dose in preventing and treating the transmission of COVID-19. The principles of mathematics are employed to analyse and investigate the dynamics of the disease. Using a qualitative prototype analysis, we acquired valuable insights into its effectiveness. One essential aspect is the basic reproduction number, a critical determinant of the disease\'s spread. This calculation is determined by studying the system\'s equilibrium and evaluating its stability. Furthermore, we examined the balance from a local and global viewpoint, considering the possibility of bifurcation and the model\'s reproductive number sensitivity index. Through numerical simulations, we have visually illustrated the analytical findings outlined in this research paper and presented a thorough examination of the efficacy of booster shots as a preventive and therapeutic measure in the spread dynamics of COVID-19.
摘要：
COVID-19疫苗已被证明可以有效地减轻由该病毒引起的疾病的生长。无论如何,接种一直是有争议的，有不同的意见和观点。这迫使一些人决定不接受疫苗。这些分歧的观点对流行病的动态和疾病的发展产生了微不足道的影响。为了应对接种疫苗的人仍然生病，许多国家已经实施了加强疫苗来进一步保护。在这个具体的调查中,一个由七个隔室组成的数学模型被用来检查加强剂量在预防和治疗COVID-19传播中的有效性。数学原理用于分析和研究疾病的动力学。使用定性原型分析，我们获得了对其有效性的宝贵见解。一个重要方面是基本繁殖数，疾病传播的关键决定因素。该计算是通过研究系统的平衡并评估其稳定性来确定的。此外，我们从本地和全球的角度考察了平衡，考虑分岔的可能性和模型的繁殖数敏感性指数。通过数值模拟,我们直观地说明了本研究论文中概述的分析结果，并全面检查了加强注射作为COVID-19传播动力学的预防和治疗措施的有效性。
