Mathematical model analysis for the transmission dynamics of bacterial meningitis disease incorporating drug-resistance class

Abstract

In this paper, a deterministic compartmental bacterial meningitis model including drug resist class is formulated. Primarily, the invariant region and positivity of solutions of the model, the equilibria and their stability are examined. The effective reproduction number (R_ef) of the system also computed using Routh-Hurwize criteria. From the stability analysis studied the disease free equilibrium (DFE) is both locally and globally asymptotically stable. The center manifold theory is used to examined the local stability of endemic equilibrium (EE), and the system shows forward bifurcation at R_ef = 1. With the help of normalized forward sensitivity index approach, the most influential parameters on the system are identified. Simulations of the model are performed using fourth-order Runge-Kutta method to demonstrate stability behaviours of DFE and EE as well as the impact of the most sensitive parameters on the bacterial meningitis disease transmission, which are presented graphically. These results showed that as time goes large trajectories of the state variables are close to DFE whenever R_ef < 1, and a unique EE when R_ef > 1, respectively. Moreover, decreasing effective transmission per contact rate, enhancing vaccine uptake rate for susceptible individuals, increasing first line treatment rate for infected and second line treatment rate for drug-resistance individuals using suitable measure mechanisms have a powerful role in reducing the burden of bacterial meningitis disease in the community.