Computational Analysis of a Fractional-Order Meningitis Transmission Model with Vaccination Using the Atangana–Baleanu–Caputo Operator

Meningitis is a significant public health problem despite the availability of effective vaccination programs, especially in children and young people. The memory-dependent features of disease transmission, immunity and vaccination dynamics are not often represented in classical integer-order epidemic models. This study proposes a fractional-order model of meningitis transmission with memory using the Atangana–Baleanu–Caputo fractional derivative. The model features susceptible, vaccinated, exposed, infectious, treated, and recovered populations to assess the impact of vaccination coverage, vaccine effectiveness, loss of vaccine immunity, and treatment on the spread of meningitis. The basic mathematical characteristics of the model, such as positivity, existence, uniqueness, and stability of solution are proven. The Laplace–Adomian Decomposition Method (LADM) is used to obtain the approximate analytical solutions, and a numerical simulation is used to analyze the influence of the fractional-order memory and epidemiological parameters on the epidemic process. The most important parameters that influence the basic reproduction number are found in sensitivity analysis to be the transmission rate and the vaccination-related parameters. The results show that simply increasing the vaccination coverage and vaccine effectiveness can substantially decrease the number of disease transmissions, and vaccine coverage can produce memory effects to change the timing and duration of outbreaks. The suggested fractional-order computational framework is a framework that is vital for studying the dynamics of meningitis and can be used for the design of long-term vaccination and disease-control strategies.