An optimal control strategy for cerebrospinal meningitis in Yobe State, Nigeria: a mathematical modeling approach

Abstract

This paper develops and analyzes a deterministic SEIHR (Susceptible-Exposed-Infectious-Hospitalized-Recovered) model to investigate the transmission dynamics of cerebrospinal meningitis (CSM) and evaluate optimal control strategies. The framework incorporates three time-dependent control variables: mass vaccination of susceptible individuals, enhanced treatment for hospitalized patients, and public awareness campaigns. Using Pontryagin's Maximum Principle, we formulate an optimal control problem to minimize the number of infected individuals and the costs associated with the interventions. The basic reproduction number ($R_0$) is derived, and its sensitivity to key parameters is analyzed. Numerical simulations, using data relevant to the Yobe State context, demonstrate that a combined strategy of early, intensive vaccination, sustained treatment efforts, and effective public awareness is the most effective approach to mitigate the burden of a CSM outbreak. These findings provide quantitative support for evidence-based public health policies aimed at controlling meningitis in high-risk regions.