MATHEMATICAL MODELING OF BACTERIAL MENINGITIS TRANSMISSION DYNAMICS: THE CASE OF ETHIOPIA

Abstract

Bacterial meningitis caused by Neisseria meningitides (Nm) is of particular concern due to its potential to cause large epidemics, causing severe brain damage and fatality. Meningitis can occur at any age but it has particularly destruction for babies and children. Mathematical modeling is the act of using mathematics to solve real life problems. The objective of this study is to develop and analyze a mathematical model for the spread of meningitis dynamics. The total population in this model is sub-divided in to five compartments, namely; Susceptible, Vaccinated, Carrier, Infected and Recovered individuals. The qualitative analysis of the SVCIR mathematical model such as; invariant region, positivity of the solution, existence and stabilities of the disease free equilibrium point and endemic equilibrium point and moreover sensitivity analysis are checked. The basic reproduction number (R0) is obtained using the next generation matrix method. The stability analysis result showed that disease free equilibrium point is locally asymptotically stable if the basic reproduction number is less than one and unstable if the basic reproduction number is greater than one. The numerical simulation was conducted using Maple 18 software in order to check the effect of basic paramerters in the expansion as well as in the control of meningitis disease. The numerical simulation results indicated that increasing the recovery rate has a great contribution to eradicate meningitis infection in the community and decreasing the transmission rate and latency rate can also have a great contribution to eliminate the meningitis. Moreover, our numerical simulation results indicated that increasing vaccination rate is vital to eradicate the meningitis disease.