A NEW MENINGITIS MATHEMATICAL MODEL AND ITS DYNAMICS

Abstract

The study develops a deterministic model with compartments for susceptible, vaccinated susceptible, uneducated carrier, educated carrier, uneducated infected, educated infected, and recovered individuals. It incorporates vaccination and education campaigns as dynamic controls for meningitis epidemic.Disease dynamics are governed by nonlinear differential equations that consider vaccination efficacy, infection progression, and recovery rates. Equilibrium states such as Disease Free and Endemic Equilibrium are analyzed to understand disease persistence and strategies for control. The basic reproduction number  is derived to assess epidemic potential and control thresholds. The meningitis model examines vaccination and education impacts. Figure 2 shows decreasing infections with higher education rates . Figures 3 and 4 illustrate the dynamics of uneducated and educated infections, stabilizing at  and respectively. For , Figure 5 indicates lower infection rates with higher vaccination.