Numerical investigation of fractional HIV-1/CTL model using Laguerre wavelet method

In this work, we investigate a mathematical perspective on HIV-1 infection, focusing on how the virus affects the Cytotoxic T Lymphocyte (CTL) response. We examine a model that illustrates the interactions between healthy CD4 (Formula presented.) T cells, latently infected cells, actively infected cells, HIV particles, and CTLs. In our scenario, a healthy T-cell can be directly infected by other cells, whether they are actively manufacturing the virus or in a dormant, latent state, as well as by a free-floating virus. We used an innovative method that employed Laguerre wavelets (LAW) to make sense of this complex web of interactions. This strategy was crucial in simplifying our theoretical problem, which we then solved numerically. We have been able to observe how the sickness behaves under various circumstances by examining this model. According to our findings, the body’s ability to produce new T-cells and the virus’s ability to disseminate are the main factors that determine how an infection turns out. Beyond that, we have discovered a more nuanced but important layer of interaction. The system is finely tuned; a small nudge to one component massively influences the army of CTLs (the cells that destroy infected cells), marking it as a major player. Similarly, we identified a beneficial trade-off where adjusting another factor simultaneously holds back the virus while giving the immune system a subtle advantage. These insights help us see the immune response not as a blunt instrument, but as a complex dance, revealing potential new steps for therapeutic intervention. The overall effect of parameter sensitivities on the model has been simulated using system sensitivities. The Caputo fractional derivative was used to investigate the model’s dynamic behaviour and complexity. A sensitivity analysis was conducted to assess how the model behaves with respect to its parameters. The findings showed that fractional solutions offer more detailed insights than the classical model. We demonstrate that the solutions to the systems are both non-negative and bounded. Numerical investigations using the Adam-Bashforth-Moulton (ABM) method and the Laguerre Wavelet Operational Matrix Method (LAWOMM) demonstrate the effectiveness of this approach. Stability and residual errors are evaluated using iterative techniques and Laguerre wavelets.