Dynamical analysis of hearing loss due to mumps virus with Caputo fractional derivative

Abstract

Mumps is the most common disease for children, which causes hearing loss in all auditory systems. WHO initiated compulsory vaccination for children who are at age of 12 months to 12 years, since 1967. Children must take two doses of vaccination for mumps. The dynamics of the system describing the mumps transmission is studied in this work. The main aim is to elucidate the nonlinear behavior of the system which can provide insights into the long-term effects of Mumps infection on auditory function. As the fractional-order derivative preserves the impact of system memory, we employ the Caputo fractional derivative as the dynamical system describing modeling to simulate hearing loss in children brought on by the mumps virus. The boundedness existence of the solution and stability analysis of the dynamical system are derived in the framework. The result is derived using a well-known numerical method to capture the corresponding consequences and predict the future consequence of the dynamical system associated with parameters. To testify to the importance of the generalizing classical model with a fractional operator, we plot 2D graphs. This study helps to researcher beginners to understand the essential and fundamental tools while investigating real-world problems.