Mathematical modeling and stability analyses on the transmission dynamics of bacterial meningitis

Abstract

Bacterial meningitis has posed a serious threat to lives and livelihood of people, especially those in the meningitis belt. This study presents a deterministic compartmental model of the disease based on SusceptibleVaccinated-Carrier-Infected-Treated-Recovered (SVCITR). This transmission process is made up of seven mutually exclusive epidemiological compartments for the transmission dynamics of the disease. The invariant region, positivity of the solutions and stability of the equilibrium points were examined using quantitative analysis. The basic reproduction number, R0 was computed using the next generation matrix approach and this was used as a threshold to establish the local and global stabilities of the model. The simulation results from the numerical simulation of the model demonstrate the effects of the model parameters on each compartment. The results show that getting people vaccinated is crucial to the control of the disease. Furthermore, the sensitivity analysis of R0 was performed in order to determine the effect of each of the model parameters in controlling the disease. Hence, reducing the values of the parameters with negative sensitivity index will help to curtail the spread of the disease.