×

Investigation of fractal-fractional HIV infection by evaluating the drug therapy effect in the Atangana-Baleanu sense. (English) Zbl 1510.92095

MSC:

92C50 Medical applications (general)
34A08 Fractional ordinary differential equations
28A80 Fractals

References:

[1] G, Dynamics of HIV variants and specific cytotoxic T-cell recognition in nonprogressors and progressors, Immunol. Lett., 57, 63-68 (1997) · doi:10.1016/S0165-2478(97)00076-X
[2] F. Kirchhoff, IV life cycle: Overview. In: T. Hope, M. Stevenson, D. Richman, (eds), Encycl. AIDS, Springer, New York, (2013), 1-9. https://doi.org/10.1007/978-1-4614-9610-6_60-1
[3] M, Anti-viral drug treatment: Dynamics of resistance in free virus and infected cell populations, J. Theor. Biol., 184, 203-217 (1997) · doi:10.1006/jtbi.1996.0307
[4] T, Drug concentration heterogeneity facilitates the evolution of drug resistance, Proc. Natl. Acad. Sci. USA, 95, 11514-11519 (1998) · Zbl 0919.92023 · doi:10.1073/pnas.95.20.11514
[5] R, Distinct effects of protease and reverse transcriptase inhibition in an immunological model of HIV-1 infection with impulsive drug effects, Bull. Math. Biol., 66, 1259-1283 (2004) · Zbl 1334.92239 · doi:10.1016/j.bulm.2003.12.004
[6] T. H. Zha, O. Castillo, H. Jahanshahi, A. Yusuf, M. O. Alassafi, F. E. Alsaadi, et al., A fuzzy-based strategy to suppress the novel coronavirus (2019-NCOV) massive outbreak, Appl. Comput. Math., 20 2021,160-176. · Zbl 1479.37096
[7] M, Study on DateJimbo-Kashiwara-Miwa equation with conformable derivative dependent on time parameter to find the exact dynamic wave solutions, Fractal Fract., 6, 1-12 (2022) · doi:10.3390/fractalfract6010004
[8] Y. M. Chu, S. Bashir, M. Ramzan, M. Y. Malik, Model-based comparative study of magnetohydrodynamics unsteady hybrid nanofluid flow between two infinite parallel plates with particle shape effects, Math. Methods Appl. Sci., 2022. http://dx.doi.org/10.1002/mma.8234 · Zbl 1538.35283
[9] M, Theoretical study of MHD electro-osmotically flow of third-grade fluid in micro channel, Appl. Math. Comput., 420, 126868 (2022) · Zbl 1510.35241 · doi:10.1016/j.amc.2021.126868
[10] Y, Combined impact of Cattaneo-Christov double diffusion and radiative heat flux on bio-convective flow of Maxwell liquid configured by a stretched nanomaterial surface, Appl. Math. Comput., 419, 126883 (2022) · Zbl 1510.76222 · doi:10.1016/j.amc.2021.126883
[11] T. H. Zhao, M. I. Khan, Y. M. Chu, Artificial neural networking (ANN) analysis for heat and entropy generation in flow of non-Newtonian fluid between two rotating disks, Math. Methods Appl. Sci., 2021. https://doi.org/10.1002/mma.7310 · Zbl 1529.76073
[12] L, Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells, Math. Biosci., 200, 44-57 (2006) · Zbl 1086.92035 · doi:10.1016/j.mbs.2005.12.026
[13] P, Modeling the drug therapy for HIV infection, J. Biol. Syst., 17, 213-223 (2009) · Zbl 1342.92103 · doi:10.1142/S0218339009002764
[14] A, A mathematical model for transmission dynamics of HIV/AIDS with effect of weak CD \(4+\) T cells, Chin. J. Phys., 56, 1045-1056 (2018) · Zbl 1543.92055 · doi:10.1016/j.cjph.2018.04.004
[15] L, Modeling within host HIV-\(1\) dynamics and the evolution of drug resistance: Trade offs between viral enzyme function and drug susceptibility, J. Theor. Biol., 247, 804-818 (2007) · Zbl 1455.92087 · doi:10.1016/j.jtbi.2007.04.014
[16] Z, Mathematical analysis of a sex-structured HIV/AIDS model with a discrete time delay, Nonlinear Anal., Theory Methods Appl., 71, 1082-1093 (2009) · Zbl 1178.34103 · doi:10.1016/j.na.2008.11.026
[17] M, Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Pade-approximation, Chaos Solitons Fractals, 134, 109686 (2020) · Zbl 1483.92149 · doi:10.1016/j.chaos.2020.109686
[18] A. S. Perelson, Modeling the interaction of the immune system with HIV, In: C. Castillo-Chavez (eds) Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomathematics, Springer, Berlin, Heidelberg, (1989), 350-370. https://doi.org/10.1007/978-3-642-93454-4_17 · Zbl 0683.92001
[19] A, Dynamics of HIV infection of CD \(4+\) T cells, Math. Biosci., 114, 81-125 (1993) · Zbl 0796.92016 · doi:10.1016/0025-5564(93)90043-A
[20] S, A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model, Appl. Math. Comput., 374, 125061 (2020) · Zbl 1433.34007 · doi:10.1016/j.amc.2020.125061
[21] D, Analysis of the model of HIV-\(1\) infection of CD \(4+\) T-cell with a new approach of fractional derivative, Adv. Differ. Equation, 2020, 1-17 (2020) · Zbl 1482.37090 · doi:10.1186/s13662-020-02544-w
[22] A, Fractional-order dynamics of Rift Valley fever in ruminant host with vaccination, Commun. Math. Biol. Neurosci., 2020, 1-32 (2020) · doi:10.28919/cmbn/5017
[23] R, Modeling the transmission of dengue infection through fractional derivatives, Chaos, Solitons Fractals, 127, 189-216 (2019) · Zbl 1448.92300 · doi:10.1016/j.chaos.2019.07.002
[24] F, Numerical solution of traveling waves in chemical kinetics: time fractional fishers equations, Fractals, 30, 22400051 (2022) · Zbl 07507535 · doi:10.1142/S0218348X22400515
[25] Y, Dynamics of fractional order COVID-19 model with a case study of Saudi Arabia, Results Phys., 21, 103787 (2021) · doi:10.1016/j.rinp.2020.103787
[26] M, The dynamics of Zika virus with Caputo fractional derivative, AIMS Math., 4, 134-146 (2019) · Zbl 1425.37054 · doi:10.3934/Math.2019.1.134
[27] A, Fractal-fractional differentiation and integtion: connecting fractal calculus and fractional calculus to predict complex system, Chaos, Solitons Fractals, 102, 396-406 (2017) · Zbl 1374.28002 · doi:10.1016/j.chaos.2017.04.027
[28] S, Mathematical analysis of HIV/AIDS infection model with Caputo-Fabrizio fractional derivative, Cogent Math. Stat., 5, 1432521 (2018) · Zbl 1438.92079 · doi:10.1080/23311835.2018.1432521
[29] S, On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana Baleanu (AB) derivative, Chaos, Solitons Fractals, 140, 110233 (2020) · Zbl 1495.92068 · doi:10.1016/j.chaos.2020.110233
[30] P, The role of prostitution on HIV transmission with memory: A modeling approach, Alexandria Eng. J., 59, 2513-2531 (2020) · doi:10.1016/j.aej.2020.04.016
[31] Z, Fractional dynamics of HIV with source term for the supply of new CD4+ T-cells depending on the viral load via Caputo-Fabrizio derivative, Molecules, 26, 1806 (2021) · doi:10.3390/molecules26061806
[32] J, Analysis of a fractional model for HIV CD \(4+\) T-cells with treatment under generalized Caputo fractional derivative, AIMS Math., 6, 7285-7304 (2021) · Zbl 1484.92042 · doi:10.3934/math.2021427
[33] Fatmawati; M., The dynamics of dengue in fection through fractal-fractional operator with real statistical data, Alexandria Eng. J., 60, 321-336 (2021) · doi:10.1016/j.aej.2020.08.018
[34] P, Approximate solution of a nonlinear fractional-order HIV model using homotopy analysis method, Int. J. Numer. Anal. Mod., 19, 52-84 (2022) · Zbl 1513.92083
[35] D, A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative, Chaos Solitons Fractals, 134, 109705 (2020) · Zbl 1483.92041 · doi:10.1016/j.chaos.2020.109705
[36] E, A fractional model of cancer-immune system with Caputo and Caputo-Fabrizio derivatives, Eur. Phys. J. Plus, 136, 1-17 (2021) · doi:10.1140/epjp/s13360-020-00966-9
[37] Z, Fractal-fractional order dynamical behavior of an HIV/AIDS epidemic mathematical model, Eur. Phys. J. Plus, 136, 1-17 (2021) · doi:10.1140/epjp/s13360-020-00994-5
[38] S. Ahmad, A. Ullah, A. Akgül, M. D. L. Sen, Study of HIV disease and its association with immune cells under nonsingular and nonlocal fractal-fractional operator, Alexandria Eng. J., (2021), 1904067. https://doi.org/10.1155/2021/1904067
[39] P, Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-\(1\) with treatment in fractional order, Phys. A: Stat. Mech. Appl., 545, 123816 (2020) · doi:10.1016/j.physa.2019.123816
[40] P, Chaotic dynamics of a fractional order HIV-\(1\) model involving AIDS-related cancer cells, Chaos, Solitons Fractals, 140, 110272 (2020) · Zbl 1495.92036 · doi:10.1016/j.chaos.2020.110272
[41] P, Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method, Chaos, Solitons Fractals, 131, 109500 (2020) · Zbl 1495.92094 · doi:10.1016/j.chaos.2019.109500
[42] M. M. El-Dessoky, M. A. Khan, Modeling and analysis of an epidemic model with fractal-fractional Atangana-Baleanu derivative, Alexandria Eng. J., 61 (2022), 729-746. https://doi.org/10.1016/j.aej.2021.04.103
[43] X. Q. Zhao, The theory of basic reproduction ratios, in Dynamical Systems in Population Biology, CMS Books in Mathematics, Springer, Cham, (2017), 285-315. https://doi.org/10.1007/978-3-319-56433-3_11 · Zbl 1393.37003
[44] C. Castillo-Chavez, Z. Feng, W. Huang, On the computation of \(R_0\) and its role on global stability, in Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, Springer, Berlin, 2002. https://doi.org/10.1007/978-1-4757-3667-0_13 · Zbl 1021.92032
[45] E, On fractional order differential equations model for nonlocal epidemics, Phys. A: Stat. Mech. Appl., 379, 607-614 (2007) · doi:10.1016/j.physa.2007.01.010
[46] S, On some extended Routh-Hurwitz conditions for fractional-order autonomous systems of order \(\alpha \in (0, 2)\) and their applications to some population dynamic models, Chaos, Solitons Fractals, 133, 109623 (2020) · Zbl 1483.34011 · doi:10.1016/j.chaos.2020.109623
[47] A. Granas, J. Dugundji, Fixed Point Theory, Springer, New York, 2003. https://doi.org/10.1007/978-0-387-21593-8 · Zbl 1025.47002
[48] D. H. Griffel, Applied Functional Analysis, Ellis Horwood: Chichester, UK, 1981. · Zbl 0461.46001
[49] A. Atangana, S. I. Araz, New Numerical Scheme with Newton Polynomial: Theory, Methods, and Applications, 1st edition, Elsevier, 2021. https://doi.org/10.1016/C2020-0-02711-8 · Zbl 1462.65001
[50] A, Quantitative image analysis of HIV-1 infection in lymphoid tissue, Science, 274, 985-989 (1996) · doi:10.1126/science.274.5289.9
[51] R, Constant mean viral copy number per infected cell in tissues regardless of high, low, or undetectable plasma HIV RNA, J. Exp. Med., 189, 1545-1554 (1999) · doi:10.1084/jem.189.10.1545
[52] P, Modeling HIV infection of CD \(4^+\) T-cell subpopulations, J. Theor. Biol., 170, 367-391 (1994) · doi:10.1006/jtbi.1994.1199
[53] H, Rapid turnover of T lymphocytes in SIV-infected rhesus macaques, Science, 279, 1223-1227 (1998) · doi:10.1126/science.279.5354.1223
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.