A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel

Aslam, Muhammad; Murtaza, Rashid; Abdeljawad, Thabet; Rahman, Ghaus ur; Khan, Aziz; Khan, Hasib; Gulzar, Haseena

doi:10.1186/s13662-021-03264-5

Cited by 41 publications

(15 citation statements)

References 25 publications

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“…Definition 2.2 (see [8]). For Θ ∈ H 1 ða, bÞ and for ω ∈ ½0, 1, the ABC-fractional integral is given by; 2 Computational and Mathematical Methods in Medicine…”

Section: Preliminariesmentioning

confidence: 99%

“…Lemma 2.2 (see [8]). Suppose that yðσÞ ∈ L p ½0, η, then the solution of fractional differential equation.…”

Section: Preliminariesmentioning

confidence: 99%

“…In conclusion, it was found that the Atangana-Baleanu fractional differential operator captures more susceptibilities while allowing for a smaller number of infections. Existence-uniqueness, stability, and simulated solutions to the HIV/AIDS infection model were analysed using the Mittag-Leffler kernel by the authors of [8]. Okyere et al [9] studied an SIR model using the Caputo derivative.…”

Section: Introductionmentioning

confidence: 99%

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Fractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate

Zhang

Addai

Ackora-Prah

et al. 2022

Computational and Mathematical Methods in Medicine

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Coinfection of Ebola virus and malaria is widespread, particularly in impoverished areas where malaria is already ubiquitous. Epidemics of Ebola virus disease arise on a sporadic basis in African nations with a high malaria burden. An observational study discovered that patients in Sierra Leone's Ebola treatment centers were routinely infected with malaria parasites, increasing the risk of death. In this paper, we study Ebola-malaria coinfections under the generalized Mittag-Leffler kernel fractional derivative. The Banach fixed point theorem and the Krasnoselskii type are used to analyse the model's existence and uniqueness. We discuss the model stability using the Hyers-Ulam functional analysis. The numerical scheme for the Ebolamalaria coinfections using Lagrange interpolation is presented. The numerical trajectories show that the prevalence of Ebolamalaria coinfections ranged from low to moderate depending on memory. This means that controlling the disease requires adequate knowledge of the past history of the dynamics of both malaria and Ebola. The graphical dynamics of the detection rate indicate that a variation in the detection rate only affects the following compartments: individuals that are latently infected with the Ebola, Ebola virus afflicted people who went unnoticed, individuals who have been infected with the Ebola virus and have been diagnosed with the disease, and persons undergoing Ebola virus therapy.

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“…Definition 2.2 (see [8]). For Θ ∈ H 1 ða, bÞ and for ω ∈ ½0, 1, the ABC-fractional integral is given by; 2 Computational and Mathematical Methods in Medicine…”

Section: Preliminariesmentioning

confidence: 99%

“…Lemma 2.2 (see [8]). Suppose that yðσÞ ∈ L p ½0, η, then the solution of fractional differential equation.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate

Zhang

Addai

Ackora-Prah

et al. 2022

Computational and Mathematical Methods in Medicine

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“…Tis study suggests using fractionalorder derivatives to investigate how COVID-19 and tuberculosis are transmitted. Worldwide, academics' interest in fractional-order derivative modeling is still very high [7][8][9][10][11][12][13][14][15][16][17][18]. Leibniz believed fractional calculus to be a paradox, yet it has since developed into a topic of interest for numerous scholars from a variety of felds.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Turberculosis‐COVID‐19 Coinfection Using Fractional Derivatives

Okyere

Ackora-Prah

Abdullah

et al. 2023

International Journal of Mathematics and Mathematical Sciences

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Fractional-order derivative modeling continues to receive great interest among researchers across the globe. In this study, Tuberculosis-COVID-19 coinfection is studied using Atangana–Baleanu fractional-order derivatives defined in Caputo sense. We confirmed the existence and singularity of the solution and investigated the model’s equilibrium points. Additionally, we examined the model’s stability in terms of the Ulam–Hyers and generalized Ulam–Hyers stability criteria. The basic reproduction number R 0 was calculated using the next-generation matrix approach. We also looked into the model’s disease-free equilibrium point’s regional stability. Numerical scheme for simulating the fractional-order system with Mittag–Leffler Kernels are presented. Numerical simulations are given to validate the model. Results of the simulation showed a decline in the number of COVID-19 infections within the population when the fractional operator was reduced.

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“…In Kumar et al (32), investigated the COVID-19 model using singular and non-singular fractional operators and compared the results of these operators. In Aslam et al (33), the authors examined a recent study on the mathematical modeling of HIV/AIDS using the Mittag-Leffler-type kernel and came to the conclusion that the infection rate decreases with decreasing operator. In Evirgen (34), the authors studied the transmission dynamics of the Nipah virus using the Caputo derivative.…”

mentioning

confidence: 99%

Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

Ngungu

Addai

Adeniji

et al. 2023

Front. Public Health

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In this study, a mathematical model for studying the dynamics of monkeypox virus transmission with non-pharmaceutical intervention is created, examined, and simulated using real-time data. Positiveness, invariance, and boundedness of the solutions are thus examined as fundamental features of mathematical models. The equilibrium points and the prerequisites for their stability are achieved. The basic reproduction number and thus the virus transmission coefficient ℜ0 were determined and quantitatively used to study the global stability of the model's steady state. Furthermore, this study considered the sensitivity analysis of the parameters according to ℜ0. The most sensitive variables that are important for infection control are determined using the normalized forward sensitivity index. Data from the United Kingdom collected between May and August 2022, which also aid in demonstrating the usefulness and practical application of the model to the spread of the disease in the United Kingdom, were used. In addition, using the Caputo–Fabrizio operator, Krasnoselskii's fixed point theorem has been used to analyze the existence and uniqueness of the solutions to the suggested model. The numerical simulations are presented to assess the system dynamic behavior. More vulnerability was observed when monkeypox virus cases first appeared recently as a result of numerical calculations. We advise the policymakers to consider these elements to control monkeypox transmission. Based on these findings, we hypothesized that another control parameter could be the memory index or fractional order.

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A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel

Cited by 41 publications

References 25 publications

Fractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate

Fractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate

Analysis of Turberculosis‐COVID‐19 Coinfection Using Fractional Derivatives

Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

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