Stability of HIV dynamic model with constraint interval parameters depending on antiretroviral treatment

The stability analysis of a microscopic model for the dynamics of the Human Immunodeficiency Virus (HIV) with antiretroviral treatment is conducted in this study, employing Constraint Interval Arithmetic (CIA) for parameter treatment. CIA enables the representation of parameters as functions with a single independent variable ranging from 0 to 1. The model is formulated through a system of four ordinary differential equations, accounting for infected CD4+ T lymphocytes, noninfected CD4+ T lymphocytes, free virus, and cytotoxic T lymphocytes. The antiretroviral treatment directly impacts the infection rate of CD4+ T lymphocytes by the virus and the reproduction rate of the virus, treated as constraint intervals. The stability analysis criterion is based on Routh–Hurwitz, where the signs of the eigenvalues of the characteristic polynomial depend on the variations of the parameters within their constraint intervals. To further explore the biological phenomenon under antiretroviral treatment, a Fuzzy Rule-Based System (FRBS) is constructed. The FRBS takes adherence to treatment by HIV-seropositive individuals and medication potency as input variables. The output variables of the FRBS correspond to values of the independent variable, determining the interval of the infection rate of CD4+ T lymphocytes by the virus and the reproduction rate of the virus. The obtained results align with existing literature when HIV-seropositive individuals undergo antiretroviral treatment, showcasing the effectiveness of the proposed model in capturing the dynamics of HIV with treatment variations.