Eur. Phys. J. Plus (2019) 134: 390
https://doi.org/10.1140/epjp/i2019-12740-9

Regular Article

Stability of a general reaction-diffusion HIV-1 dynamics model with humoral immunity

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia

^* e-mail: a_m_elaiw@yahoo.com

Received: 8 March 2019
Accepted: 8 May 2019
Published online: 13 August 2019

Abstract

This paper studies the global stability of a six-dimensional system of PDEs that describes the HIV-1 dynamics with humoral immune response and heterogeneous diffusion. The model contains some parameters that measure the efficiency of highly active antiretroviral therapies (HAART). The model also comprises three kinds of infected cells 1) latently infected cells which do not produce HIV-1 virions, but can be activated to produce viruses; 2) short-lived productively infected cells that are characterized by living for a short period of time and creating large amounts of HIV-1 particles; 3) long-lived productively infected cells that are characterized by having a long life and producing small amounts of HIV-1 virions. The production, infection and death rates of all compartments are given by general functions. The non-negativity and boundedness of the solutions are discussed. The global stability conditions for the infection-free equilibrium, humoral-inactivated equilibrium, and humoral-activated equilibrium are investigated by building suitable Lyapunov functionals. Some numerical simulations are executed to support the theoretical results and show the spatiotemporal evolution of the solutions.