Modelling the transmission behavior of measles disease considering contaminated environment through a fractal-fractional Mittag-Leffler kernel
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Date
2024-05
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Publisher
IOP Publishing
Abstract
This work utilises a fractal-fractional operator to examine the dynamics of transmission of measles
disease. The existence and uniqueness of the measles model have been thoroughly examined in the
context of the fixed point theorem, specifically utilising the Atangana-Baleanu fractal and fractional
operators. The model has been demonstrated to possess both Hyers-Ulam stability and Hyers-Ulam
Rassias stability. Furthermore, a qualitative analysis of the model was performed, including
examination of key parameters such as the fundamental reproduction number, the measles-free and
measles-present equilibria, and assessment of global stability. This research has shown that the
transmission of measles disease is affected by natural phenomena, as changes in the fractal-fractional
order lead to changes in the disease dynamics. Furthermore, environmental contamination has been
shown to play a significant role in the transmission of the measles disease.
Description
This article is published by IOP Publishing 2024 and is also available at https://doi.org/10.1088/1402-4896/ad51b0
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Citation
Phys. Scr. 99 (2024) 075025