Modelling Meningitis Transmission with Booster Vaccination and Resistance Dynamics: Equilibrium and Control Analyses

Meningitis remains a global health threat due to its high fatality, epidemic potential, and rising antibiotic resistance. While mathematical models exist, previous studies often neglected the combined dynamics of booster vaccination waning and antibiotic resistance evolution, limiting their ability to inform optimal control strategies. To bridge this gap, we develop a novel deterministic compartmental model incorporating six epidemiological compartments, distinct primary/booster vaccination pathways with waning immunity, and resistance emergence via mutation. Using equilibrium analysis and stability theory (Routh-Hurwitz, Lyapunov functions), we establish critical thresholds: the basic reproduction number ($R_0$) determines disease extinction ($R_0 < 1$) or endemicity ($R_0 > 1$), and both meningitis-free and endemic equilibria are globally stable when $R_0 < 1$ and $R_0 > 1$, respectively. Sensitivity analysis via next-generation matrices reveals that $R_0$ is most significantly influenced by contact rates ($\alpha_m$, $\alpha_r$), vaccination rates ($\kappa$, $\chi$), recovery rates ($\tau_m$, $\tau_r$), and the resistance mutation rate ($\xi$). Crucially, our results demonstrate that increasing booster coverage ($\chi > 0.15$) and reducing resistance mutation ($\xi < 0.01$) are paramount for driving $R_0 < 1$. Combining interventions (booster durability, neonatal immunisation $\kappa > 0.25$, resistance containment) provides synergistic, non-linear reductions in transmission. This model explicitly integrates booster dynamics and resistance and emergence, provides a realistic framework for optimising vaccination programs and antibiotic stewardship, particularly in settings like the African Meningitis Belt, aligning with WHO roadmap targets.