A fractional mathematical model of heartwater transmission dynamics considering nymph and adult amblyomma ticks

Asamoah, Joshua Kiddy K.; Fatmawati, Fatmawati

doi:10.1016/j.chaos.2023.113905

Cited by 20 publications

(2 citation statements)

References 35 publications

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“…The disorder can occasionally prove fatal. In the study of [37], they investigated the Caputo fractional version of disease transmission in domestic ruminants and amblyomma ticks. The positivity and boundedness criteria were derived using the Laplace transform.…”

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%

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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“…Fractional calculus has gained much more attention in recent years in an effort to better understand the previously outlined procedure. Due to its dynamic features, which have demonstrated a range of applications in real-world scenarios, including biological and physical processes, it has become more and more popular (see [16]). Fractional calculus has a long history, just like conventional calculus (see [17]).…”

Section: Introductionmentioning

confidence: 99%

Study of Rotavirus Mathematical Model Using Stochastic and Piecewise Fractional Differential Operators

Alharthi,

Jeelani

2023

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This manuscript is related to undertaking a mathematical model (susceptible, vaccinated, infected, and recovered) of rotavirus. Some qualitative results are established for the mentioned challenging childhood disease epidemic model of rotavirus as it spreads across a population with a heterogeneous rate. The proposed model is investigated using a novel approach of fractal calculus. We compute the boundedness positivity of the solution of the proposed model. Additionally, the basic reproduction ratio and its sensitivity analysis are also performed. The global stability of the endemic equilibrium point is also confirmed graphically using some available values of initial conditions and parameters. Sufficient conditions are deduced for the existence theory, the Ulam–Hyers (UH) stability. Specifically, the numerical approximate solution of the rotavirus model is investigated using efficient numerical methods. Graphical presentations are presented corresponding to a different fractional order to understand the transmission dynamics of the mentioned disease. Furthermore, researchers have examined the impact of lowering the risk of infection on populations that are susceptible and have received vaccinations, producing some intriguing results. We also present a numerical illustration taking the stochastic derivative of the proposed model graphically. Researchers may find this research helpful as it offers insightful information about using numerical techniques to model infectious diseases.

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A non-linear mathematical model for typhoid fever transmission dynamics with medically hygienic compartment

Lawal,

Yusuf,

Abidemi

et al. 2024

Model. Earth Syst. Environ.

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A fractional mathematical model of heartwater transmission dynamics considering nymph and adult amblyomma ticks

Cited by 20 publications

References 35 publications

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

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

Study of Rotavirus Mathematical Model Using Stochastic and Piecewise Fractional Differential Operators

A non-linear mathematical model for typhoid fever transmission dynamics with medically hygienic compartment

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