A theoretical and numerical analysis of a fractal–fractional two-strain model of meningitis

Abstract

Meningitis is an inflammation of the membranes that surround and protect the brain and spinal cord. Typically, the enlargement is caused by a bacterial or viral infection of the fluid around the brain and spinal cord. For many years, licensed vaccinations against meningococcal, pneumococcal, and Haemophilus influenzae diseases have been accessible. Vaccines are meant to protect against the most dangerous strains of these germs, which are known as serotypes or serogroups. There have been significant increases in strain coverage and vaccine availability throughout time, but there is no universal vaccine against these illnesses. In this study, we explore the mathematical features of a new six-compartmental fractal–fractional two-strain model of meningitis. With the use of compact functions and ϕ−ψ-contractions, we establish the existence of solutions. To study the unique solutions, we employ the Banach principle. On the basis of the Hyers-Ulam definition for the fractal–fractional two-strain model of meningitis, stable solutions are examined. From the numerical simulations, we notice that as the fractal–fractional order decreases, the number of infected individuals with strain 1 of meningitis decreases, while the number of infected individuals with strain 2 rises. This means that all serotypes or serogroups need to be controlled effectively for the disease to be closed up.