We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe dynamics of HIV-AIDS infection. The infection process is modelled by a general functional response and memory effect described Caputo derivative. Stability instability equilibrium points are determined terms basic reproduction number. Furthermore, optimal control system ...

The purpose of this note is to introduce the key concepts in the mathematical modelling of HIV/AIDS. The note starts with a brief introduction to epidemiological and modelling terminology. It then presents a basic model of HIV transmission, and discusses how this model can be improved to allow for greater accuracy in modelling of HIV transmission and survival under HIV infection. Finally, the e...

We review mathematical models of HIV dynamics, disease progression, and therapy. We start by introducing a basic model of virus infection and demonstrate how it was used to study HIV dynamics and to measure crucial parameters that lead to a new understanding of the disease process. We discuss the diversity threshold model as an example of the general principle that virus evolution can drive dis...

This paper shows how mathematical methods can be implemented to formulate guidelines for clinical testing and monitoring of HIV/AIDS disease. First, a mathematical model for HIV infection is presented which the measurement of the CD4T cells and the viral load counts are needed to estimate all its parameters. Next, through an analysis of model properties, the minimal number of measurement sample...

In this article, we present a fractional order HIV-1 infection model of CD4+ T-cell. We analyze the effect of the changing the average number of the viral particle N with initial conditions of the presented model. The Laplace Adomian decomposition method is applying to check the analytical solution of the problem. We obtain the solutions of the fractional order HIV-1 model in the form of infini...

Global stability is analyzed for a general mathematical model of HIV-1 pathogenesis proposed by Nelson and Perelson [11]. The general model include two distributed intracellular delays and a combination therapy with a reverse transcriptase inhibitor and a protease inhibitor. It is shown that the model exhibits a threshold dynamics: if the basic reproduction number is less than or equal to one, ...

Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1-2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal...

Many aspects of the complex interaction between human immunodeficiency virus type 1 (HIV-1) and the human immune system remain elusive. Our objective was to study these interactions, focusing on the specific roles of dendritic cells (DCs). DCs enhance HIV-1 infection processes as well as promote an antiviral immune response. We explored the implications of these dual roles. A mathematical model...