Mathematical modeling of infectious diseases and the impact of vaccination strategies.

Mathematical modeling plays a crucial role in understanding and combating infectious diseases, offering predictive insights into disease spread and the impact of vaccination strategies. This paper explored the significance of mathematical modeling in epidemic control efforts, focusing on the interplay between vaccination strategies, disease transmission rates, and population immunity. To facilitate meaningful comparisons of vaccination strategies, we maintained a consistent framework by fixing the vaccination capacity to vary from 10 to 100% of the total population. As an example, at a 50% vaccination capacity, the pulse strategy averted approximately 45.61% of deaths, while continuous and hybrid strategies averted around 45.18 and 45.69%, respectively. Sensitivity analysis further indicated that continuous vaccination has a more direct impact on reducing the basic reproduction number $ R_0 $ compared to pulse vaccination. By analyzing key parameters such as $ R_0 $, pulse vaccination coefficients, and continuous vaccination parameters, the study underscores the value of mathematical modeling in shaping public health policies and guiding decision-making during disease outbreaks.