A generalized fractional HIV-1 infection model with humoral immunity and highly active antiretroviral therapy

Abstract

Highly active antiretroviral therapy (HAART) is a treatment that uses a combination of three or more drugs to treat human immunodeficiency virus type 1 (HIV-1). On the other hand, immunological memory is an important characteristic of humoral immunity. In this paper, we propose a mathematical model that takes into account immunological memory to describe the dynamics of HIV-1 infection in the presence of such therapy. We first show that the developed model is mathematically and biologically well posed. Furthermore, we discuss the existence of equilibrium points and their stability. Both effects of HAART and memory on the dynamical behavior of our proposed model are rigorously investigated. In addition, numerical simulations are presented to illustrate our analytical findings.