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

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.