Dynamical Analysis of Posttreatment HIV-1 Infection Model

Abstract

This paper aims to explore the dynamic characteristics of the post treatment human immunodeficiency virus (HIV) type-1 model by proposing the theoretical frameworks. Distinct from the previous works, this study explores the effect of effector cells, loss of functional effector cells, and two types of anti-retroviral therapies such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs) and also the effect of intracellular time delay. Based on the Routh—Hurwitz criterion and eigenvalue analysis, the stability of the proposed HIV-1 model is analyzed. To reveal the significance of time delay, the Hopf-type bifurcation analysis is performed. The optimal control algorithm is designed by choosing the antiviral therapies such as RTI and PI as control parameters. Numerical simulations are performed to validate the effectiveness of the proposed theoretical frameworks.