Media campaigns, early diagnosis, isolation and treatment on bacterial meningitis outbreak prevention: A modeling study

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, S I a I s M R S , 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, R e f , which includes contributions from asymptomatic R e f a and symptomatic individuals R e f s . We derive the basic reproduction number, R 0 , 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 e f a and R e f 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.