Bacterial meningitis is a severe infection affecting the protective membranes of the brain and spinal cord, with rapidly worsening symptoms that can lead to life-threatening complications. This study presents an autonomous deterministic epidemic model, SIaIsMRS, to explore the dynamics of bacterial meningitis in a community implementing control
strategies like media coverage, early diagnosis, isolation, and treatment. We adjust the transmission probability based on media coverage and calculate the effective reproduction
number, Ref , which includes contributions from asymptomatic $R_ef^a$ and symptomatic individuals $R_ef^s$ . We derive the basic reproduction number, R0, to characterize
initial infection spread and analyze the local stability of infection-free and endemic equilibria, using the Routh-Hurwitz criteria. For global stability, we apply Castillo-Chavez method for the infection-free equilibrium and the Lyapunov functional technique for the endemic equilibrium, after a uniform persistence study. A local sensitivity analysis evaluates the impact of each parameter on the threshold dynamical parameters $R_{ef}^a$ and $R_{ef}^s$ . We also explore an optimal control problem using Pontryagin’s maximum principle. The paper concludes with numerical simulations that bridge theoretical and numerical findings.

Mathematical analysis, optimal control, bacterial meningitis, early diagnosis, media coverage, numerical results