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.

Riaz, M., Raza, N., Martinovic, J., Bakar, A., Kurkcu, H., Tunç, O. (2024). Fractional dynamics and sensitivity analysis of measles epidemic model through vaccination. ARAB JOURNAL OF BASIC AND APPLIED SCIENCES, 31(1), 265-281 [10.1080/25765299.2024.2345424].

### Fractional dynamics and sensitivity analysis of measles epidemic model through vaccination

#### 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.
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Articolo in rivista - Articolo scientifico
Atangana-Baleanu derivative; measles; numerical analysis; sensitivity analysis; Ulam-Hyers stability;
English
7-mag-2024
2024
31
1
265
281
open
Riaz, M., Raza, N., Martinovic, J., Bakar, A., Kurkcu, H., Tunç, O. (2024). Fractional dynamics and sensitivity analysis of measles epidemic model through vaccination. ARAB JOURNAL OF BASIC AND APPLIED SCIENCES, 31(1), 265-281 [10.1080/25765299.2024.2345424].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/476220`