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Analysis of Fractional Order Mathematical Modelling of HFMD Transmission through ABC Derivative

Aakash Mohandoss, Gunasundari Chandrasekar

Mathematica Applicanda

2023

Vol. 51, no. 2

199--221

The mathematical modelling of Hand, Foot, and Mouth Disease (HFMD) transmission using fractional-order calculus, especially the Atangana-Baleanu derivative, is investigated in this paper. HFMD is a viral illness that usually affects premature children and can have serious consequences. Conventional models based on integer-order derivatives have limitations in capturing the intricate dynamics of HFMD transmission accurately. Fractional-order calculus is employed in this study to enhance the modelling precision by incorporating memory and hereditary effects into the system. The Atangana-Baleanu derivative is used to explain fractional differentiation, allowing for a more accurate representation of disease processes. The proposed model is analyzed using analytical techniques to evaluate its stability, existence, and uniqueness. The findings contribute to an improved understanding of HFMD transmission dynamics and provide insights into effective control strategies for disease mitigation. In this work, the use of Atangana-Baleanu derivative indicates their potential for improving the accuracy as well as validity of mathematical models.

Stabilność i zbieżność modelu gradientowego w interaktywnej optymalizacji wizualnej w trybie bezpośrednim

Makles K.

Metody Informatyki Stosowanej

2011

nr 4

135-146

The article describes the stability and convergence criterion of linear gradient internal model used in on-line interactive optimization. This type of optimization, in fact of increasing computing power of modern computers, allows to solve incompletely determined optimization problems. Stability and convergence of the linear gradient model was discused for three cases: when searching point moving from the forbidden into the allowed area, when searching point moving in the allowed area, and whensearching point moving from the allowed into the forbidden area.

Stability in the case of incomplete model information

Radziszewski B.

Vibrations in Physical Systems

2002

Vol. 20

248--249