Optimization of an effective method for a model of HIV infection of CD4$^{+}$ T-cells

  • Hossein Hassani Shahrekord University
  • José António Tenreiro Machado
  • Eskandar Naraghiras


This study proposes an optimization method based on a set of basis functions (denoted as transcendental Bernstein series (TBS)) that includes the free coefficients and control parameters for solving a model of HIV infection of CD4$^{+}$ T-cells (HIV-CD4T). The solution of the model is expanded in terms of the TBS. First, the new operational matrices for derivatives are derived. Then, the Lagrange multipliers are applied for converting the model HIV-CD4T into a simpler problem requiring the solution of an algebraic equations system in the unknown coefficients and parameters. Additionally, the convergence of the proposed method is analyzed. To illustrate the accuracy of the method, two examples are tested and the approximate solutions compared with those obtained by other numerical approaches.