A fractal–fractional order model for exploring the dynamics of Monkeypox disease

Wireko, Fredrick Asenso; Adu, Isaac Kwasi; Sebil, Charles; Asamoah, Joshua Kiddy K.

doi:10.1016/j.dajour.2023.100300

Cited by 1 publication

(1 citation statement)

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“…Recently, in the work of Wireko et. al [48], the monkeypox disease was studied through the use of fractal-fractional operators where it was reported that the memory effect exhibited by many biological structures are better observed through the use of the mixture of fractal dimensions and fractional operators. Also, Adu et al [49] studied ebola with reinfection and reported in their work that the biological changes in the structure of the ebola virus is well captured through the use of a fractal dimension and a fractional operator concurrently.…”

Section: Introductionmentioning

confidence: 99%

Modelling the transmission behavior of measles disease considering contaminated environment through a fractal-fractional Mittag-Leffler kernel

Wireko,

Adu,

Gyamfi

et al. 2024

Phys. Scr.

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This work utilises a 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 \textcolor{blue}{Hyers-Ulam} stability and \textcolor{blue}{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 \textcolor{blue}{measles}-free and measles-present equilibria, and assessment of global stability. This research has shown that the transmission of \textcolor{blue}{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 \textcolor{blue}{measles} disease. } 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 lam 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.

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Section: Introductionmentioning

confidence: 99%