Özdek, Demet2025-07-252025-07-2520251598-58651865-2085https://doi.org/10.1007/s12190-025-02594-xThe main purpose of this study is to explore the impact of problem parameters on three different models of Human Immunodeficiency Virus (HIV) infection. The first model is the most widely studied HIV infection model, involving three groups: uninfected T cells (T), infected T cells (I), and free virus particles (V). The second model includes an additional parameter that accounts for the effect of the cure rate. The third model extends the first by dividing infected cells into two subgroups—latently and actively infected T cells—and thus includes four nonlinear differential equations. These nonlinear systems are solved using the Lucas wavelet method, which offers significant advantages, such as ease of implementation in symbolic computation and effective numerical results. We solve the models for several parameter values and discuss the impact of these parameters on the course of HIV infection in detail. Due to the absence of an analytical solution, we examine the accuracy through residual error calculation and compare our results with other numerical results available in the literature, presenting them in the form of tables and figures. © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2025.eninfo:eu-repo/semantics/closedAccessHIV Infection ModelsCure RateLatently Infected T CellsNonlinear SystemsLucas WaveletsArticle10.1007/s12190-025-02594-x2-s2.0-105010657401