A Deterministic Mathematical Model of Meningitis Transmission Dynamics with Vaccination and Screening

This study aims to examine the mathematical model of meningitis transmission as a deterministic model. The model includes five compartments: susceptible (S), carrier (C), infected (I), treatment (T), and recovered (R). We also consider vaccination and screening as interventions in disease transmission. In this work, we obtained two equilibrium points: disease-free equilibrium point and endemic equilibrium point. The next generation matrix is employed to compute the basic reproduction numbers (R₀). We also analyzed the sensitivity of parameters concerning R₀. If R₀ < 1, then the disease-free equilibrium point exists and is locally stable, whereas the endemic equilibrium point exists when R₀ > 1 and is locally stable if the Routh-Hurwitz criterion is satisfied. We use the Runge-Kutta 4th order method to confirm the stability properties of the equilibrium points and also show that vaccination and screening affect the transmission dynamics of Meningitis