Unveiling the dynamics of meningitis infections: a comprehensive study of a novel fractional-order model with optimal control strategies

This study explores the transmission dynamics of meningitis by developing a bisusceptible model using Caputo fractional-order operator. Our goals are to enhance the understanding of meningitis disease and implement effective community control measures. The model takes into account the impacts of health conditions in susceptible and vaccinated population on the disease dynamics. We rigorously analyze the introduced fractional-order model, validating properties like existence, uniqueness, nonnegativity, and boundedness of the solutions. The stability analysis of equilibrium states of the model is presented with detailed examination of the associated stability regions in the parameters’ space. Bifurcation analysis is carried out to investigate qualitative changes in dynamical behaviors of the model. The basic reproduction number $(R_{0})$ is determined, then we perform sensitivity analysis to identify the influences of key parameters’ variations. For optimal and cost-effective management of adequate control measures, we update some constant parameters to be time-dependent variables and formulate a suggested fractional optimal control problem. Using Pontryagin’s maximum principle, the necessary optimality conditions are derived to achieve our goals. Different strategies for optimal control measures are employed and evaluated. The work can help policymakers run protection programs efficiently at low cost and also support the achievement of Sustainable Development Goals in health sectors. Numerical simulations verify the attained theoretical results and reveal that the proposed control measures can effectively eradicate the infection at minimum costs.