Fractional dynamics and sensitivity analysis of measles epidemic model through vaccination


Riaz M. B., Raza N., Martinovic J., Bakar A., Kurkcu H., Tunç O.

Arab Journal of Basic and Applied Sciences, vol.31, no.1, pp.265-281, 2024 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1080/25765299.2024.2345424
  • Journal Name: Arab Journal of Basic and Applied Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.265-281
  • Keywords: Atangana-Baleanu derivative, measles, numerical analysis, sensitivity analysis, Ulam-Hyers stability
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

Measles is a highly contagious disease that mainly affects children worldwide. Even though a reliable and effective vaccination is available, there were 140,000 measles deaths worldwide in 2018, and most of them were children under the age five years. In this paper, we comprehensively investigate a novel fractional SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) model of the measles epidemic powered by nonlinear fractional differential equations to understand the epidemic’s dynamical behaviour. We use a non-singular Atangana-Baleanu fractional derivative to analyze the proposed model, taking advantage of non-locality. The existence, uniqueness, positivity and boundedness of the solutions are shown via concepts of fixed point theory, and we also perform the Ulam-Hyers stability of the considered model. The parameter sensitivity is discussed in the context of the variance with each parameter using 3-D graphics based on the basic reproduction number. Moreover, with the Atangana-Toufik numerical scheme, numerical findings are depicted for different fractional-order values. The presented approach produce results that are efficiently consistent and in excellent agreement with the theoretical results.