Mathematical Modeling and Stability Analysis of HIV Infection Dynamics in T-Cells Using Differential Equations

Abstract

HIV infection remains a major global health challenge due to its ability to target and deplete CD4+ T-cells, a critical

component of the immune system. This study develops a mathematical model using a system of differential equations to

describe the dynamics of normal, latently infected, and actively infected T-cells, as well as free viral particles. The model

identifies two biologically significant steady states: a virus-free (uninfected) state and an endemic infectionstate where the

virus persists. Analytical methods, including the Routh-Hurwitz stability criteria, are employed to examine the conditions

under which each steady state is stable. The results show that the virus-free state is attainable if the number of virions

produced per infected T-cell remains below a critical threshold, whereas the endemic state emerges when viral replication

surpasses this threshold. This framework provides insights into HIV progression, immune response dynamics, and the

impact of therapeutic strategies, offering a quantitative basis for predicting disease outcomes and evaluating potential

interventions.