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ARTICLE

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Saima Rashid^1,2,*, Fahd Jarad^3,4

1 Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan
2 Department of Natural Sciences, School of Arts and Sciences, Lebanese American University, Beirut, 11022801, Lebanon
3 Department of Mathematics, Faculty of Arts and Science, Çankaya University, Ankara, 06790, Turkey
4 Department of Medical Research, China Medical University, Taichung, 40402, Taiwan

* Corresponding Author: Saima Rashid. Email:

(This article belongs to the Special Issue: Recent Developments on Computational Biology-I)

Computer Modeling in Engineering & Sciences 2024, 139(3), 2289-2327. https://doi.org/10.32604/cmes.2023.028773

Received 06 January 2023; Accepted 09 June 2023; Issue published 11 March 2024

Abstract

Because of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions. Several numerical simulations for various fractional orders and randomization intensities are illustrated.

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