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Analytical and numerical study of the HIV-1 infection of \(\mathrm{CD}4^+\) T-cells conformable fractional mathematical model that causes acquired immunodeficiency syndrome with the effect of antiviral drug therapy. (English) Zbl 1531.92070


MSC:

92D30 Epidemiology
34A08 Fractional ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
Full Text: DOI

References:

[1] Abdel‐GawadHI, TantawyM, MachadoJT. Abundant structures of waves in plasma transitional layer sheath. Chin J Phys. 2020;67:147‐154. · Zbl 07833171
[2] KumarVS, RezazadehH, EslamiM, IzadiF, OsmanMS. Jacobi elliptic function expansion method for solving KdV equation with conformable derivative and dual‐power law nonlinearity. Int J Appl Comput Math. 2019;5(5):127. · Zbl 1431.35155
[3] YuW, ZhangH, ZhouQ, BiswasA, AlzahraniAK, LiuW. The mixed interaction of localized, breather, exploding and solitary wave for the (3 + 1)‐dimensional Kadomtsev-Petviashvili equation in fluid dynamics. Nonlinear Dyn. 2020;100(2):1611‐1619.
[4] LuD, TariqKU, OsmanMS, BaleanuD, YounisM, KhaterMMA. New analytical wave structures for the (3 + 1)‐dimensional Kadomtsev‐Petviashvili and the generalized Boussinesq models and their applications. Results Phys. 2019;14:102491.
[5] LiuJG, OsmanMS, WazwazAM. A variety of nonautonomous complex wave solutions for the (2 + 1)‐dimensional nonlinear Schrödinger equation with variable coefficients in nonlinear optical fibers. Optik. 2019;180:917‐923.
[6] RaoJ, MihalacheD, ChengY, HeJ. Lump‐soliton solutions to the Fokas system. Phys Lett A. 2019;383(11):1138‐1142. · Zbl 1475.35110
[7] LuD, OsmanMS, KhaterMMA, AttiaRAM, BaleanuD. Phys A: Stat Mech Appl. 2020;537:122634.
[8] DingY, OsmanMS, WazwazAM. Abundant complex wave solutions for the nonautonomous Fokas-Lenells equation in presence of perturbation terms. Optik. 2019;181:503‐513.
[9] El‐SherifAA, ShoukryMM, Abd‐ElgawadMM. Protonation equilibria of some selected a‐amino acids in DMSO‐water mixture and their Cu (II)‐complexes. J Solut Chem. 2013;42(2):412‐427.
[10] AslaKA, AbdelkarimmAT, Abu El‐ReashGM, El‐SherifAA. Potentiometric, thermodynamics and DFT calculations of some metal (II)‐Schiff base complexes formed in solution. Int J Electrochem Sci. 2020;15(4):3891‐3913.
[11] KumarS, KumarA, SametB, Gómez‐AguilarJF, OsmanMS. A chaos study of tumor and effector cells in fractional tumor‐immune model for cancer treatment. Chaos Sol Fract. 2020;141:110321. · Zbl 1496.92034
[12] AliKK, Abd El SalamMA, MohamedEM, SametB, KumarS, OsmanMS. Numerical solution for generalized nonlinear fractional integro‐differential equations with linear functional arguments using Chebyshev series. Adv Diff Eq. 2020;2020:494. · Zbl 1486.65289
[13] RazaN, OsmanMS, Abdel‐AtyAH, Abdel‐KhalekS, BesbesHR. Optical solitons of space‐time fractional Fokas-Lenells equation with two versatile integration architectures. Adv Diff Eq. 2020;2020:517. · Zbl 1486.35371
[14] ChenLP, YinH, YuanLG, LopesAM, MachadoJT, WuRC. A novel color image encryption algorithm based on a fractional‐order discrete chaotic neural network and DNA sequence operations. Front Inf Technol Electr Eng. 2020;21(6):866‐879.
[15] OsmanMS, RezazadehH, EslamiM. Traveling wave solutions for (3 + 1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Nonl Eng. 2019;8(1):559‐567.
[16] OsmanMS, RezazadehH, EslamiM, NeiramehA, MirzazadehM. Analytical study of solitons to Benjamin-Bona-Mahony-Peregrine equation with power law nonlinearity by using three methods. Univ Politehnica Bucharest Scient Bull‐Ser A‐Appl Math Phys. 2018;80(4):267‐278. · Zbl 1438.35365
[17] XuSL, ZhouQ, ZhaoD, BelicMR, ZhaoY. Spatiotemporal solitons in cold Rydberg atomic gases with Bessel optical lattices. Appl Math Lett. 2020;106:106230. · Zbl 1439.78015
[18] InanB, OsmanMS, AkT, BaleanuD. Analytical and numerical solutions of mathematical biology models: the Newell-Whitehead-Segel and Allen-Cahn equations. Math Meth Appl Sci. 2020;43(5):2588‐2600. · Zbl 1454.35397
[19] KayumMA, AkbarMA, OsmanMS. Competent closed form soliton solutions to the nonlinear transmission and the low‐pass electrical transmission lines. Europ Phys J Plus. 2020;135(7):1‐20.
[20] NuruddeenRI, AboodhKS, AliKK. Analytical investigation of soliton solutions to three quantum Zakharov-Kuznetsov equations. Commun Theor Phys. 2018;70(4):405.
[21] AliKK, NuruddeenRI, RaslanKR. New structures for the space‐time fractional simplified MCH and SRLW equations. Chaos, Sol Fract. 2018;106:304‐309. · Zbl 1392.35326
[22] RaslanKR, AliKK, ShallalMA. The modified extended tanh method with the Riccati equation for solving the space‐time fractional EW and MEW equations.Chaos Sol Fract. 2017;103:404‐409. · Zbl 1375.35608
[23] Abdel‐GawadHI, OsmanM. Exact solutions of the Korteweg‐de Vries equation with space and time dependent coefficients by the extended unified method. Indian J Pure Appl Math. 2014;45(1):1‐12. · Zbl 1307.35251
[24] RaslanKR, El‐DanafTS, AliKK. Exact solution of the space‐time fractional coupled EW and coupled MEW equations. European Phys J Plus. 2017;132(7):319.
[25] AliKK, NuruddeenRI, RaslanKR. New hyperbolic structures for the conformable time‐fractional variant bussinesq equations. Opt Quant Electron. 2018;50(2):61.
[26] BaleanuD, OsmanMS, ZubairA, RazaN, ArqubOA, MaWX. Soliton solutions of a nonlinear fractional Sasa-Satsuma equation in Monomode optical fibers. Appl Math Inf Sci. 2020;14(3):1‐10.
[27] AliKK, WazwazAM, OsmanMS. Optical soliton solutions to the generalized nonautonomous nonlinear Schrödinger equations in optical fibers via the sine‐Gordon expansion method. Optik. 2020;208:164132.
[28] Abdel‐GawadHI, OsmanMS. On the variational approach for analyzing the stability of solutions of evolution equations. Kyungpook Math J. 2013;53(4):661‐680. · Zbl 1297.65058
[29] Abdel‐GawadHI, ElazabNS, OsmanM. Exact solutions of space dependent Korteweg-de Vries equation by the extended unified method. J Phys Soc Jpn. 2013;82(4):044004.
[30] CulshawRV, RuanS, WebbG. A mathematical model of cell‐to‐cell spread of HIV‐1 that includes a time delay. J Math Biology. 2003;46(5):425‐444. · Zbl 1023.92011
[31] BaleanuD, MohammadiH, RezapourS. Analysis of the model of HIV‐1 infection of CD4^+ T‐cell with a new approach of fractional derivative. Adv Diff Eq. 2020;2020(1):1‐17. · Zbl 1482.37090
[32] AkT, OsmanMS, KaraAH. Polynomial and rational wave solutions of Kudryashov-Sinelshchikov equation and numerical simulations for its dynamic motions. J Appl Anal Comput. 2020;10(5):2145‐2162. · Zbl 1461.35084
[33] RaslanKR, EL‐DanafTS, AliKK. Finite difference method with different high order approximations for solving complex equation. New Trends Math Sci. 2017;5(1):114‐127.
[34] AliKK, CattaniC, Gómez‐AguilarJF, BaleanuD, OsmanMS. Analytical and numerical study of the DNA dynamics arising in oscillator‐chain of Peyrard-Bishop model. Chaos, Sol Fract. 2020;139:110089. · Zbl 1490.92009
[35] GaoW, BaskonusHM, ShiL. New investigation of bats-hosts-reservoir-people coronavirus model and application to 2019‐nCoV system. Adv Diff Eq. 2020;2020:391. · Zbl 1485.92129
[36] AtanganaA. Modelling the spread of COVID‐19 with new fractal‐fractional operators: can the lockdown save mankind before vaccination?Chaos, Sol Fract. 2020;136:109860.
[37] KhanMA, AtanganaA. Modeling the dynamics of novel coronavirus (2019‐nCov) with fractional derivative. Alex Eng J. 2020;59(4):2379‐2389.
[38] GaoW, VeereshaP, BaskonusHM, PrakashaDG, KumarP. A new study of unreported cases of 2019‐nCOV epidemic outbreaks. Chaos, Sol Fract. 2020;138:109929.
[39] GoufoEFD, KhanY, ChaudhryQA. HIV and shifting epicenters for COVID‐19, an alert for some countries. Chaos, Sol Fract. 2020;139:110030.
[40] GaoW, VeereshaP, PrakashaDG, BaskonusHM. Novel dynamic structures of 2019‐nCoV with nonlocal operator via powerful computational technique. Biology. 2020;9(5):107.
[41] ChenTM, RuiJ, WangQP, ZhaoZY, CuiJA, YinL. A mathematical model for simulating the phase‐based transmissibility of a novel coronavirus. Infect Dis Poverty. 2020;9(1):24.
[42] CattaniC, PierroG. On the fractal geometry of DNA by the binary image analysis. Bull Math Biol. 2013;75(9):1544‐1570. · Zbl 1272.92013
[43] OwolabiKM, AtanganaA. Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative. Chaos, Sol Fract. 2019;126:41‐49. · Zbl 1448.34022
[44] AtanganaA. Application of fractional calculus to epidemiology. Fractional Dynamic. Berlin; 2015:174‐190.
[45] İlhanE, KiymazIO. A generalization of truncated M‐fractional derivative and applications to fractional differential equations. Appl Math Nonl Sci. 2020;5(1):171‐188. · Zbl 07664125
[46] CattaniC. A review on harmonic wavelets and their fractional extension. J Adv Eng Comput. 2018;2(4):224‐238.
[47] ZhangY, CattaniC, YangXJ. Local fractional homotopy perturbation method for solving non‐homogeneous heat conduction equations in fractal domains. Entropy. 2015;17:6753‐6764.
[48] YangAM, ZhangYZ, CattaniC, et al. Application of local fractional series expansion method to solve Klein-Gordon equations on Cantor sets. Abstr Appl Anal. 2014;2014:6. Article ID 372741. · Zbl 1472.35342
[49] CattaniC, SrivastavaHM, YangXJ. Fractional Dynamics. Berlin: Walter de Gruyter; 2015.
[50] YangXJ. General Fractional Derivatives: Theory, Methods and Applications. New York: CRC Press; 2019. · Zbl 1417.26001
[51] YangXJ, GaoF, JuY. General Fractional Derivatives with Applications in Viscoelasticity. Cambridge, Massachusetts: Academic Press; 2002.
[52] Xiao‐JunXJ, SrivastavaHM, MachadoJT. A new fractional derivative without singular kernel. Therm Sci. 2016;20(2):753‐756.
[53] YangAM, HanY, LiJ, LiuWX. On steady heat flow problem involving Yang-Srivastava-Machado fractional derivative without singular kernel. Therm Sci. 2016;20(3):717‐721.
[54] YangXJ, RagulskisM, TahaT. A new general fractional‐order derivative with Rabotnov fractional‐exponential kernel. Therm Sci. 2019;23(6B):3711‐3718.
[55] YangXJ. New rheological problems involving general fractional derivatives with nonsingular power‐law kernels. Proc Roman Acad Ser A‐Math Phys Tech Sci Inf Sci. 2018;19(1):45‐52.
[56] CaoY, ZhangY, WenT, LiP. Research on dynamic nonlinear input prediction of fault diagnosis based on fractional differential operator equation in high‐speed train control system. Chaos: Interdiscipl J Nonl Sci. 2019;29(1):013130.
[57] YangXJ. New general calculi with respect to another functions applied to describe the Newton‐like dashpot models in anomalous viscoelasticity. Therm Sci. 2019;23(6B):3751‐3751.
[58] YangXJ, GaoF, JingHW. New mathematical models in anomalous viscoelasticity from the derivative with respect to another function view point. Therm Sci. 2019;23(3A):1555‐1561.
[59] YangXJ. New non‐conventional methods for quantitative concepts of anomalous rheology. Therm Sci. 2019;23(6B):4117‐4127.
[60] AgostoLM, HerringMB, MothesW, HendersonAJ. HIV‐1‐infected CD4+ T cells facilitate latent infection of resting CD4+ T cells through cell‐cell contact. Cell Rep. 2018;24(8):2088‐2100.
[61] RuelasDS, GreeneWC. An integrated overview of HIV‐1 latency. Cell. 2013;155(3):519‐529.
[62] SunY, ClarkEA. Expression of the c‐myc proto‐oncogene is essential for HIV‐1 infection in activated T cells. J Exper Med. 1999;189(9):1391‐1398.
[63] DananeJ, AllaliK, HammouchZ. Mathematical analysis of a fractional differential model of HBV infection with antibody immune response. Chaos, Sol Fract. 2020;136:109787. · Zbl 1489.92145
[64] AmeenI, BaleanuD, AliHM. An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment. Chaos, Sol Fract. 2020;137(202):109892. · Zbl 1489.92134
[65] AtanganaA. Fractional discretization: the African’s tortoise walk. Chaos, Sol Fract. 2020;130:109399.
[66] AtanganaA. Blind in a commutative world: simple illustrations with functions and chaotic attractors. Chaos, Sol Fract. 2018;114:347‐363. · Zbl 1415.34009
[67] SinghJ, KumarD, HammouchZ, AtanganaA. A fractional epidemiological model for computer viruses pertaining to a new fractional derivative. Appl Math Comput. 2018;316:504‐515. · Zbl 1426.68015
[68] YokuşA, GülbaharS. Numerical solutions with linearization techniques of the fractional Harry Dym equation. Appl Math Nonl Sci. 2019;4(1):35‐42. · Zbl 1506.65133
[69] OwolabiKM, HammouchZ. Spatiotemporal patterns in the Belousov-Zhabotinskii reaction systems with Atangana-Baleanu fractional order derivative. Phys A: Stat Mech Appl. 2019;523:1072‐1090. · Zbl 07563440
[70] AtanganaA. Fractal‐fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos, Sol Fract. 2017;102:396‐406. · Zbl 1374.28002
[71] KiymazO, CetinkayaA. Variational iteration method for a class of nonlinear differential equations. Int J Contemp Math Sci. 2010;5(37):1819‐1826. · Zbl 1223.34009
[72] Al‐GhafriKS, RezazadehH. Solitons and other solutions of (3 + 1)‐dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation. Appl Math Nonl Sci. 2019;4(2):289‐304. · Zbl 1506.35258
[73] KiymazO, CetinkayaA. The solution of the time‐fractional diffusion equation by the generalized differential transform method. Math Comput Model. 2013;57(9‐10):2349‐2354. · Zbl 1286.65180
[74] BrzezińskiDW. Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus. Appl Math Nonl Sci. 2018;3(2):487‐502. · Zbl 1515.65320
[75] KiymazO, CetinkayaA, AgarwalP. An extension of Caputo fractional derivative operator and its applications. J Nonl Sci Appl. 2013;9:3611‐3621. · Zbl 1345.26014
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