MATHEMATICAL MODELING ON THE TRANSMISSION DYNAMICS OF MENINGITIS

ABSTRACT A comprehensive mathematical model for meningitis transmission dynamics is presented in this work. Utilizing a system of ordinary differential equations, the work examined model behavior across endemic and disease-free equilibria. Stability analysis identified prerequisites for disease persistence and control, revealing a stable disease free equilibrium point when , a stable global asymptotic state when and a stable endemic equilibrium point whenever . The model systematically tracked population transitions through different disease stages: susceptible, exposed, untreated and treated infected, treatment, weakened immune, recovered, and reinfection vulnerable compartments. Sensitivity analysis highlighted key factors affecting disease spread, particularly transmission rates β, exposure rates σ, and progression rates α₁ and α₂. Numerical simulations demonstrated how varying transmission parameters impact population dynamics, emphasizing the complex interactions within the epidemiological system. The results underscore the necessity of targeted public health interventions, including enhanced screening, treatment strategies, and population-level disease management approaches.