Estimation of HIV infection mathematical model]{Estimation of HIV infection mathematical model parameters using modified LHPM

Document Type : Original Article


1 Department of Mathematics, Roudehen Branch, Islamic Azad University, Roudehen, Iran

2 Department of Mathematics, Qom University of Technology (QUT), Qom, Iran


In this paper, modified laplace homotopy perturbation method(LHPM) is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems model for HIV infection . Mathematical models have proven valuable in understanding the dynamics of HIV infection. By comparing these models to data obtained from patients undergoing antiretroviral drug therapy, it has been possible to determine many quantitative features of the interaction between HIV, the virus that causes AIDS, and the cells that are infected by the virus. We apply modified LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. When we do not know the exact solution of a given problem, generally we use the RK4 method for comparison since it is widely used and accepted. Comparison of the results with RK4 method is confirmed that modified LHPM performs with very high accuracy. Results show that modified LHPM is a very promising method for obtaining approximate solutions to the model for HIV. The results validate the accuracy and efficiency of the proposed method for the approximate solution of the HIV infection model.


Main Subjects

[1] M.J. Ahmed, W. Al-Hayani, The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities, Al-Rafidain Journal of Computer Sciences and Mathematics, 16(2) 2022, 61-70.
[2] O. Akpa ,B. Oyejola, Modeling the transmission dynamics of HIV/AIDS epidemics: an introduction and a review, J. Infection Developing Countries, 4 2010, 597-608.
[3] N. Anjum, J.H. He, Two Modifications of the Homotopy Perturbation Method for Nonlinear Oscillators, J. Appl. Comput. Mech, 6 2020, 1420-1425.
[4] Attaullah, M. Sohaib, Mathematical modeling and numerical simulation of HIV infection model, Results in Applied Mathematics, 7 2020, 100-118.
[5] J. Biazar, H. Ghazvini, Convergence of the homotopy perturbation method for partial differential equations, Nonlinear Analysis: Real World Applications, 10 2009, 2633-2640.
[6] M. Bodnar, The nonnegativity of solutions of delay differential equations, Appl Math Lett, 13 2000, 91-95.
[7] J.H. He, Homotopy perturbation method: A new nonlinear analytical technique, Applied Mathematics and Computation, 135 2003, 73-79.
[8] J.H. He, Recent development of the homotopy perturbation method, Topol. Methods Nonlinear Anal, 31 2008, 205-209.
[9] J.H. He, Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computation, 135(1) 2003, 73-79.
[10] A. Kimbir,H. Oduwole, A mathematical model of HIV/AIDS Transmission Dynamics Considering Counseling and Antiretroviral Therapy, J. Modern Math Stat, (2) 2008, 166-169.
[11] S. Malik, I. Qureshi, M. Amir, A. Malik, Nature inspired computational approach to solve the model for HIV infection of CD4+T-cells, Res J Recent Sci, 3(6) 2014, 67-76.
[12] M.S. Mechee, G.A. Al-Juaifri ,A.K. Joohy, Modified homotopy perturbation method for solving generalized linear complex differential equations, Applied Mathematical Sciences, 11(51) 2017, 2527-2540.
[13] M. Medan, Homotopy perturbation method for solving a model for HIV infection of CD4+ T-cells, Istanb Tipcart Univ Fen Balmier Derris Yell, 12 2007, 39-52.
[14] M. Medan, A. Gkdogan and A. Yildirim, On the numerical solution of the model for HIV infection of CD4+T-cells, Comput Math Appl, 62 2011, 118-123.
[15] A. Necib, A. Merad, Laplace transform and homotopy perturbation methods for solving the pseudo hyperbolic integrodifferential problems with purely integral conditions, Kragujevac Journal of Mathematics, 44(2) 2020, 251-272.
[16] V.K. Srivastava, M.K. Awasthi, S. Kumar, Numerical approximation for HIV infection of CD4+ T cells mathematical model, Ain Shams Engineering Journal, 5(2) 2012, 625-629.