Analytical and Numerical Solutions of a TB-HIV/AIDS Co-infection Model via Fractional Derivatives Without Singular Kernel

Dokuyucu, Mustafa Ali; Dutta, Hemen

doi:10.1007/978-3-030-49896-2_7

Cited by 4 publications

(5 citation statements)

References 18 publications

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“…In Theorem 3.3, X(t), Y(t), Z(t) were shown to have a unique solution. Let X(t), Y(t), Z(t) be an approximate solution of system (13) satisfying the system (19). Then, we can say that…”

Section: Stability Analysismentioning

confidence: 99%

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Analysis of a fractional tumor-immune interaction model with exponential kernel

Ali

Dutta

2021

Filomat

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In this paper, a tumor-immune interaction model has been analyzed via Caputo-Fabrizio fractional derivative operator with exponential kernel. Existence of solution of the model has been established with a fixed-point method and then it demonstrated the uniqueness of solution also. The stability of the model has been analyzed with the help of Hyers-Ulam stability approach and then numerical solution by using the Adam-Basford method. The results are further examined in detail with simulations for different fractional derivative values.

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“…In Theorem 3.3, X(t), Y(t), Z(t) were shown to have a unique solution. Let X(t), Y(t), Z(t) be an approximate solution of system (13) satisfying the system (19). Then, we can say that…”

Section: Stability Analysismentioning

confidence: 99%

“…They conducted research on the regression of cancer with chemotherapy and thus the necessity to move it to a region where it controls cancer. In addition, there are many studies in the literature on mathematical modeling and its fractional derivatives [11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a fractional tumor-immune interaction model with exponential kernel

Ali

Dutta

2021

Filomat

Self Cite

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“…Different nonlinear therapeutic rates between diseases are possible. The nonlinear incidence and treatment rate can be very helpful in assisting health organizations identify effective treatments that will stop the spread of the disease [9] .…”

Section: Introductionmentioning

confidence: 99%

Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women

Batool,

Farman,

Ahmad

et al. 2024

AIMSPH

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<abstract> <p>Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved.</p> </abstract>

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“…Wu et al [15] studied the cellular dynamics of the HIV-1 with uncertainty in the initial data. Dokuyucu and Dutta [16] studied the TB-HIV dynamics with the fractional order derivative. Te order of the fractional derivative contributes to the memory efects.…”

Section: Introductionmentioning

confidence: 99%

Fractional Derivative Model for Analysis of HIV and Malaria Transmission Dynamics

Cheneke

2023

Discrete Dynamics in Nature and Society

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In this study, a Caputo fractional derivative is employed to develop a model of malaria and HIV transmission dynamics with optimal control. Also, the model’s basic properties are shown, and the basic reproduction number is computed using the next-generation matrix method. Additionally, the order of fractional derivative analysis shows that the infected group decreases at the beginning for the higher-order of fractional derivative. Moreover, the early activation of memory effects through public health education reduces the impact of malaria and HIV infections on further progression and transmission. On the other hand, effective optimal controls reduce the occurrence and prevalence of HIV and malaria infections from the beginning to the end of the investigation. Finally, the numerical simulations are done for the justification of analytical solutions with numerical solutions of the model. Moreover, the MATLAB platform is incorporated for numerical simulation of the solutions.

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Analytical and Numerical Solutions of a TB-HIV/AIDS Co-infection Model via Fractional Derivatives Without Singular Kernel

Cited by 4 publications

References 18 publications

Analysis of a fractional tumor-immune interaction model with exponential kernel

Analysis of a fractional tumor-immune interaction model with exponential kernel

Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women

Fractional Derivative Model for Analysis of HIV and Malaria Transmission Dynamics

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