The African meningitis belt (AMB) countries experience recurring epidemics of \textit{Neisseria meningitidis} (Nm) meningococcal meningitis. This study presents a Susceptible-Carrier-Infected-Recovered (SCIR)-based dynamic model to analyze Nm transmission dynamics in this region, incorporating the impact of pentavalent vaccines. The model serves as a foundational tool for evaluating the effectiveness of these vaccines and aiding decision-making in control and prevention efforts.We examine various aspects of Nm infection epidemiology, focusing on the introduction of pentavalent meningococcal conjugate vaccines targeting serogroups A, C, W-135, Y, and X in AMB countries. Our analysis includes assessing different vaccination strategies for carriers with and without vaccine-covered serogroups, as well as evaluating disease transmissibility and infectivity in high- and low-risk areas.One of the main quantitative findings in our study is identifying the impact of significant decrease in the number of carriers with the implementation of pentavalent vaccines. This reduction underscores the efficacy of these vaccination strategies in reducing Nm transmission and controlling epidemics in these regions.Additionally, important epidemiological parameters such as reproduction numbers are derived to inform effective prevention measures. Climate change, socioeconomic disparities, and population density are identified as potential drivers of increased Nm outbreaks in these countries. However, further research is necessary to better understand disease variability and vulnerability, especially in young children.