A Fractional Order Model for the Transmission Dynamics of Meningococcal Meningitis With Real Statistical Data

Abstract

ABSTRACT In this paper, we propose a Caputo‐based fractional‐order derivative model for the transmission dynamics of meningococcal meningitis (MM), incorporating the environmental concentration of Neisseria meningitidis as well as factors such as vaccination and the hygiene consciousness of susceptible individuals. The existence and uniqueness of solutions to the model are established using Banach's and Schauder's fixed‐point theorems. Additionally, we compute the basic reproduction number and examine the local asymptotic stability of the disease‐free equilibrium using the Routh–Hurwitz criterion. We analyze the stability of the fractional‐order meningitis model using the Ulam–Hyers–Rassias stability method. Furthermore, we fit the model to the cumulative confirmed cases of cerebrospinal meningitis in Nigeria using data obtained from the Nigeria Centre for Disease Control (NCDC) to validate the model. The model demonstrates a good fit with the reported cumulative cases. Numerical simulations are conducted for various values of the fractional order. The results reveal an inverse relationship between the fractional order and the total number of asymptomatic infected individuals (carriers), symptomatic infected individuals, and the environmental concentration of Neisseria meningitidis. This implies that increasing the order of the fractional derivative leads to a decrease in the number of infections and bacterial concentration. Moreover, increasing vaccine uptake and improving hygiene consciousness among susceptible individuals significantly reduce both the number of infections and the environmental concentration of Neisseria meningitidis.