An efficient method to solve the mathematical model of HIV infection for CD8+ T-cells

In this paper, the mathematical model of HIV infection for CD8+ T-cells is illustrated. The homotopy analysis method and the Laplace transformations are combined for solving this model. Also, the convergence theorem is proved to demonstrate the abilities of presented method for solving non-linear mathematical models. The numerical results for N = 5, 10 are presented. Several h-curves are plotted to show the convergence regions of solutions. The plots of residual error functions indicate the precision of presented method.

[1]  M. Nowak,et al.  Immune Responses and Viral Phenotype: Do Replication Rate and Cytopathogenicity Influence Virus Load? , 2000 .

[2]  Devendra Kumar,et al.  Numerical computation of Klein–Gordon equations arising in quantum field theory by using homotopy analysis transform method , 2014 .

[3]  Chun Wang,et al.  A one-step optimal homotopy analysis method for nonlinear differential equations , 2010 .

[4]  Y. Tan,et al.  A General Approach to Obtain Series Solutions of Nonlinear Differential Equations , 2007 .

[5]  S. Noeiaghdam.  Solving a non-linear model of HIV infection for CD4+T cells by combining Laplace transformation and Homotopy analysis method , 2018, 1809.06232.

[6]  Carsten Magnus,et al.  Modelling the Course of an HIV Infection: Insights from Ecology and Evolution , 2012, Viruses.

[7]  M. A. Araghi,et al.  Homotopy analysis transform method for solving generalized Abel's fuzzy integral equations of the first kind , 2015, 2015 4th Iranian Joint Congress on Fuzzy and Intelligent Systems (CFIS).

[8]  D Greenhalgh,et al.  Mathematical modelling of the spread of HIV/AIDS amongst injecting drug users. , 1997, IMA journal of mathematics applied in medicine and biology.

[9]  S. Abbasbandy,et al.  Analysis of Forced Convection in a Circular Tube Filled With a Darcy–Brinkman–Forchheimer Porous Medium Using Spectral Homotopy Analysis Method , 2011 .

[10]  2D FLOW OF CASSON FLUID WITH NON-UNIFORM HEAT SOURCE/SINK AND JOULE HEATING , 2018, Frontiers in Heat and Mass Transfer.

[11]  Rachel Waema Mbogo,et al.  Mathematical Modelling of In-Vivo Dynamics of HIV Subject to the Influence of the CD8+ T-Cells , 2017 .

[12]  Mohammad Ali Fariborzi,et al.  Valid implementation of the Sinc-collocation method to solve linear integral equations by the CADNA library , 2019 .

[13]  S. Abbasbandy,et al.  New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology , 2013 .

[14]  Huazhong Shu,et al.  Numerical solutions of partial differential equations by discrete homotopy analysis method , 2010, Appl. Math. Comput..

[15]  Rishi Kumar Pandey,et al.  Homotopy analysis Sumudu transform method for time—fractional third order dispersive partial differential equation , 2016, Advances in Computational Mathematics.

[16]  Samad Noeiaghdam.  A novel technique to solve the modified epidemiological model of computer viruses , 2019 .

[17]  M. A. Araghi,et al.  Discrete Homotopy Analysis Method for Solving Linear Fuzzy Differential Equations , 2015 .

[18]  Samad Noeiaghdam,et al.  A Valid Scheme to Evaluate Fuzzy Definite Integrals by Applying the CADNA Library , 2017, Int. J. Fuzzy Syst. Appl..

[19]  S. Abbasbandy,et al.  Predictor Homotopy Analysis Method (Pham) for Nano Boundary Layer Flows with Nonlinear Navier Boundary Condition: Existence of Four Solutions , 2014 .

[20]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[21]  Ahmet Yildirim,et al.  On the numerical solution of the model for HIV infection of CD4+ T cells , 2011, Comput. Math. Appl..

[22]  S. Abbasbandy,et al.  Fractional Homotopy Analysis Transforms Method for Solving a Fractional Heat-Like Physical Model , 2015 .

[23]  Saeid Abbasbandy,et al.  Predictor homotopy analysis method: Two points second order boundary value problems , 2014 .

[24]  Emran Khoshrouye Ghiasi,et al.  Constructing analytic solutions on the Tricomi equation , 2018 .

[25]  Majid Khan,et al.  A novel solution procedure for fuzzy fractional heat equations by homotopy analysis transform method , 2012, Neural Computing and Applications.

[26]  Majid Khan,et al.  A novel analytical solution of a fractional diffusion problem by homotopy analysis transform method , 2012, Neural Computing and Applications.

[27]  Emran Khoshrouye Ghiasi,et al.  Analytical and Numerical Solutions to the 2 D Sakiadis Flow of Casson Fluid with Cross Diffusion , Inclined Magnetic Force , Viscous Dissipation and Thermal Radiation Based on Buongiorno ' s Mathematical Model , 2019 .

[28]  R. Saleh,et al.  Homotopy analysis method for the Sakiadis flow of a thixotropic fluid , 2019, The European Physical Journal Plus.

[29]  M. A. Araghi,et al.  Finding optimal step of fuzzy Newton-Cotes integration rules by using the CESTAC method , 2017 .

[30]  Nonlinear stability and thermomechanical analysis of hydromagnetic Falkner–Skan Casson conjugate fluid flow over an angular–geometric surface based on Buongiorno’s model using homotopy analysis method and its extension , 2018, Pramana.

[31]  F. Santonja,et al.  Solving a model for the evolution of smoking habit in Spain with homotopy analysis method , 2013 .

[32]  Muhammad Suleman,et al.  Solving a modified nonlinear epidemiological model of computer viruses by homotopy analysis method , 2018, Mathematical Sciences.

[33]  Songxin Liang,et al.  Laplace transform for the solution of higher order deformation equations arising in the homotopy analysis method , 2013, Numerical Algorithms.

[34]  Iqtadar Hussain,et al.  A new comparative study between homotopy analysis transform method and homotopy perturbation transform method on a semi infinite domain , 2012, Math. Comput. Model..

[35]  Shijun Liao,et al.  On the homotopy analysis method for nonlinear problems , 2004, Appl. Math. Comput..

[36]  Sushila,et al.  A Novel Approach for Thin Film Flow Problem Via Homotopy Analysis Sumudu Transform Method , 2012, SocProS.

[37]  Devendra Kumar,et al.  Fractional modelling for BBM-Burger equation by using new homotopy analysis transform method , 2014 .

[38]  Samad Noeiaghdam,et al.  Numerical approximation of modified non-linear SIR model of computer viruses , 2019, Contemporary Mathematics.

[39]  L. Yakob.  Endectocide-treated cattle for malaria control: A coupled entomological-epidemiological model , 2015, Parasite Epidemiology and Control.

[40]  Saeid Abbasbandy,et al.  Newton-homotopy analysis method for nonlinear equations , 2007, Appl. Math. Comput..

[41]  L. Luboobi,et al.  Stochastic Model for In-Host HIV Dynamics with Therapeutic Intervention , 2013 .

[42]  S. Abbasbandy,et al.  Predictor homotopy analysis method and its application to some nonlinear problems , 2011 .

[43]  M A Nowak,et al.  Viral dynamics in hepatitis B virus infection. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[44]  M. A. Araghi,et al.  A novel technique based on the homotopy analysis method to solve the first kind Cauchy integral equations arising in the theory of airfoils , 2016 .

[45]  Saeed Kazem,et al.  A modification of the homotopy analysis method based on Chebyshev operational matrices , 2013, Math. Comput. Model..

[46]  Shijun Liao,et al.  Homotopy Analysis Method in Nonlinear Differential Equations , 2012 .

[47]  R. Saleh,et al.  Unsteady shrinking embedded horizontal sheet subjected to inclined Lorentz force and Joule heating, an analytical solution , 2018, Results in Physics.

[48]  Peeyush Chandra,et al.  Modeling the dynamics of HIV and CD4+ T cells during primary infection , 2010 .

[49]  Hasan Barzegar Kelishami,et al.  Homotopy analysis transform method for solving Abel’s integral equations of the first kind , 2016 .

[50]  R. Saleh,et al.  Non-Dimensional Optimization of Magnetohydrodynamic Falkner–Skan Fluid Flow , 2018, INAE Letters.

[51]  V. Sizikov,et al.  Control of accuracy on Taylor-collocation method to solve the weakly regular Volterra integral equations of the first kind by using the CESTAC method , 2018, 1811.09802.

[52]  C. M. Dias,et al.  An Optimal Control Approach to HIV Immunology , 2015 .

[53]  Ş. Yüzbaşı.  A numerical approach to solve the model for HIV infection of CD4+T cells , 2012 .

[54]  M. A. Araghi.  HOMOTOPY REGULARIZATION METHOD TO SOLVE THE SINGULAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND , 2018 .

[55]  Dumitru Baleanu,et al.  Laplace homotopy analysis method for solving linear partial differential equations using a fractional derivative with and without kernel singular , 2016 .

[56]  Saeid Abbasbandy,et al.  Finding optimal convergence control parameter in the homotopy analysis method to solve integral equations based on the stochastic arithmetic , 2018, Numerical Algorithms.