Global Analysis of Meningitis Disease With Optimal Control

Abstract

The meningitis epidemic has impacted lives negatively, especially in Sub-Sahara Africa, dubbed the ‘Meningitis Belt’. The epidemic has been a public health concern due to an improper understanding of the disease’s dynamics. To implement a control measure that will help minimize the epidemic, we introduce a non-linear Meningitis model that describes the dynamic behaviour of the disease and explains the transmission trend. The model explores the condition that leads to local or global asymptomatic stability of the equilibria. The model is subjected to a sensitivity analysis to find the parameters that influence the R0. The model is modified into an optimal control by adding timedependent controls. The control model is solved qualitatively using Pontryagin’s maximum principle and numerically using MATLAB and the fourth-order Runge-Kutta method. We provide a control strategy that can be relied on for management decision-making based on the results.