On solutions of time fractional order random HIV/AIDS modelling

Year 2024, Volume: 42 Issue: 6, 1899 - 1906, 09.12.2024

Mehmet Merdan , Selami Öktem

Abstract

In this study, The fractional random HIV/AIDS model approximate analytical solutions were produced using the differential transformation method. The approximate analytical solution of the fractional order Random HIV/AIDS model was obtained with the help of the differential transformation method. For the fractional random HIV/AIDS model, which was created by choosing the initial conditions from the exponential, beta, and normal distributions, graphic simulations of the expected value, variance, and confidence intervals of the most com-monly used probability characteristics were obtained with the help of the MATLAB package program. Results obtained are interpreted.

Keywords

Fractional HIV/AIDS Model, Expected Value, Variance, Confidence Intervals

References

• REFERENCES [1] World Health Organization. HIV. 2022. Available at: https://www.who.int/news-room/factsheets/detail/hiv-aids Last Accessed Date: 19.02.2022.
• [2] Worobey M, Gemmel M, Teuwen DE, Haselkorn T, Kunstman K, Bunce M. Direct evidence of extensive diversity of HIV-1 in Kinshasa by 1960. Nature 2008;455:661–664. [CrossRef]
• [3] Clavel F, Guétard D, Brun-Vézinet F, Chamaret S, Rey MA, Santos-Ferreira MO, Montagnıer L. Isolation of a new human retrovirus from West African patients with AIDS. Science 1986;233:343–346. [CrossRef]
• [4] Burgard M, Jasseron C, Matheron S, Damond F, Hamrene K, Blanche S. Mother-to-child transmission of HIV-2 infection from 1986 to 2007 in the ARNS French Perinatal Cohort EPF-CO1. Clin Infect Dis 2010;51:833–843. [CrossRef]
• [5] Xuanpei Z, Wenshuang L, Fengying W, Xuerong M. Dynamics of an HIV/AIDS transmission model with protection awareness and fluctuations. Chaos Solit Fract 2023;169. [CrossRef]
• [6] Vyambwera M. Mathematical modelling of the HIV/AIDS epidemic and the eff ect of public health education. Unpublished master's thesis. Cape Town: Western Cape University; 2014.
• [7] Kirschner D. Using mathematics to understand HIV ımmune dynamics. Notices Am Math Soc 1996;43:191–202.
• [8] Emvudu Y, Bongor D. Mathematical analysis of a HIV/AIDS model with treatment. IEJPAM 2012;4.
• [9] Lüleci G. Solution of the initial boundary value problem for the fractional diffusion equation. Unpublished master's thesis. Kocaeli: Kocaeli Üniversitesi; 2019.
• [10] Samko SG, Kilbas AA, Marichev OI. Fractional İntegrals and Derivatives Theory and Applications. Yverdon: Gordon ve Breach; 1993.
• [11] Miller KS, Ross B. An Introduction to The Fractional Calculus and Fractional Differential Equations. London: John Wiley & Sons; 1993.
• [12] İbiş B. Numerical solutions of differential-algebraic equations of fractional order. Unpublished doctoral thesis. İstanbul: Yıldız Technical University; 2011.
• [13] Podlubny I. Fractional differential equations. San Diego, USA: Academic Press; 1998.
• [14] Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations. Philadelphia, USA: Elsevier Science; 2006.
• [15] Caputo M. Elasticita e Dissipazione. Bolonga: Zanichelli; 1969.
• [16] Zhou J. Differential transformation and its applications for electrical circuits. Wuhan, China: Borneo Huazhong University Press; 1986.
• [17] Pukhov GE. Computational structure for solving differential equations by Taylor transformations. Cybernt Syst Anal 1978;14:383–390. [CrossRef]
• [18] Ayaz F. Solutions of the system of differential equations by differential transform method. Appl Math Comput 2004;147:547–567. [CrossRef]
• [19] El-Metwally H, Sohaly MA, Elbaz IM. Stochastic global exponential stability of disease-free equilibrium of HIV/AIDS model. Eur Phys J Plus 2020;135:840. [CrossRef]
• [20] Erbaş OS. Probability and Statistics. Ankara: Gazi Kitabevi; 2020.
• [21] Feller W. An Introduction to Probability Theory and Its Applications. 3rd ed. New York, USA: John Wiley & Sons; 1968.
• [22] Merdan M, Anac H, Bekiryazici Z, Kesemen T. Solving of some random partial differential equations by using differential transformation method and laplace-padé method. J Gumushane Univ Inst Sci Technol 2019;9:108–118.
• [23] Merdan M, Şişman Ş. Analysıs of random discrete time logistic model. Sigma J Eng Nat Sci 2020;38:1269–1298.
• [24] Merdan M, Altay Ö, Bekiryazici Z. Investigation of the behaviour of volterra ıntegral equations with random effects. J Gumushane Univ Inst Sci Technol 2020;10:205–216. [CrossRef]
• [25] Bekiryazıcı Z, Kesemen T, Merdan M, Khaniyev T. Modeling disease transmission dynamics with random data and heavy tailed random effects: The Zika case. TWMS J App Eng Math 2023;13:1272– 1286.
• [26] Şengül S, Bekiryazıcı Z, Merdan M. Wong-Zakai approximation for stochastic models of smoking, Sigma J Eng Nat Sci 2023;41:958–968. [CrossRef]
• [27] Merdan M, Atasoy N. On the solutions of fractional random ordinary differential equations with the Residual power series method, Alexandria Eng J 2023;70:169–177. [CrossRef]
• [28] Jamil S, Farman M, Akgül A. Qualitative and quantitative analysis of a fractal fractional HIV/AIDS model, Alexandria Eng J 2023;76:167–177. [CrossRef]
• [29] Xu C, Liu Z, Pang Y, Akgül A, Baleanu D. Dynamics of HIV-TB coinfection model using classical and Caputo piecewise operator: A dynamic approach with real data from South-East Asia, European and American regions. Chaos Solit Fract 2022;165:112879. [CrossRef]
• [30] Farman M, Akgül A, Tekin MT, Akram MM, Ahmad A, Mahmoud EE, et al. Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel. Alexandria Eng J 2022;61:10965–10980. [CrossRef]
• [31] Liu X, Ahmad S, Rahman M, Nadeem Y, Akgül A. Analysis of a TB and HIV co-infection model under Mittag-Leffler fractal-fractional derivative. Phys Script 2022;97:054011. [CrossRef]
• [32] Ahmad S, Ullah A, Akgül A, De la Sen M. Study of HIV Disease and Its Association with Immune Cells under Nonsingular and Nonlocal Fractal-Fractional Operator, Complexity 2021;2021:1904067. [CrossRef]