Modelling on COVID-19 control with double and booster-dose vaccination

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.