A Mathematical Model for Allergic Reactions Induced by the Therapy of HIV

ABSTRACT A new mathematical model for cell evolution in HIV is introduced and studied. Delay differential equations are used to capture the dynamics of immune system cells involved in allergies, as well as the evolution of HIV viruses, infected and uninfected CD4 cells, and cytotoxic T‐lymphocytes, under specific antiretroviral therapy. The model extends prior work by incorporating time delays to reflect the latency in immune response and drug effects, as well as interactions between the immune system and viral dynamics. Essential qualitative properties of the solutions, such as nonnegativity and global existence, are proved, ensuring the biological feasibility of the model. A partial stability analysis is conducted for some steady states of the system using Lyapunov‐Krasovskii functionals. Biological interpretation of partial stability results are given and the interplay between infected cells and immune responses during HIV treatment is further explored, with a particular focus on mitigating allergic reactions induced by medication. Numerical simulations are employed to illustrate the impact of these interactions and evaluate the effectiveness of treatment strategies.