Fractional Dynamics of an Infection Model With Time-Varying Drug Exposure

Abstract

We introduce a fractional order model for the human immunodeficiency virus (HIV) dynamics, where time-varying drug exposure and drug resistance are assumed. We derive conditions for the local and global asymptotic stability of the disease-free equilibrium. We find periodic stable endemic states for certain parameter values, for sinusoidal drug efficacies, and when considering a density-dependent decay rate for the T cells. Other classes of periodic drug efficacies are considered and the effect of the phases of these functions on the dynamics of the model is also studied. The order of the fractional derivative plays an important role in the severity of the epidemics.