Related papers: Heterogeneous Viral Environment in a HIV Spatial M…
We consider a spatially-heterogeneous generalization of a well-established model for the dynamics of the Human Immunodeficiency Virus-type 1 (HIV) within a susceptible host. The model consists of a nonlinear system of three coupled…
A dynamic model of non-lineal time-dependent ordinary differential equations (ODE) has been applied to the interactions of a HIV infection with the immune system cells. This model has been simplified into two compartments: lymph node and…
We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diffusion in a two-dimensional environment. The model consists of two ODEs for…
In this paper, we investigate a novel 3-compartment model of HIV infection of CD4$^+$ T-cells with a mass action term by including two versions: one baseline ODE model and one delay-differential equation (DDE) model with a constant discrete…
This research gives a thorough examination of an HIV infection model that includes quiescent cells and immune response dynamics in the host. The model, represented by a system of ordinary differential equations, captures the complex…
Mathematical modeling of biological systems is crucial to effectively and efficiently developing treatments for medical conditions that plague humanity. Often, systems of ordinary differential equations are a traditional tool used to…
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability…
We study within-host HIV dynamics using a three--component nonlinear ordinary differential equation model for healthy CD4$^{+}$ T cells, infected CD4$^{+}$ T cells, and free virus. In addition to the baseline model without treatment, we…
In this work we introduce a differential equation model with time-delay that describes the three-stage dynamics and the two time scales observed in HIV infection. Assuming that the virus has high mutation and rapid reproduction rates that…
HIV dynamical models are often based on non-linear systems of ordinary differential equations (ODE), which do not have analytical solution. Introducing random effects in such models leads to very challenging non-linear mixed-effects models.…
We have developed a mathematical model for in-host virus dynamics that includes spatial chemotaxis and diffusion across a two dimensional surface representing the vaginal or rectal epithelium at primary HIV infection. A linear stability…
We construct a seven-component model of the in-host dynamics of the Human Immunodeficiency Virus Type-1 (i.e, HIV) that accounts for latent infection and the propensity of viral mutation. A dynamical analysis is conducted and a theorem is…
One way in which the human immunodeficiency virus (HIV-1) replicates within a host is by infecting activated CD4+ T-cells, which then produce additional copies of the virus. Even with the introduction of antiretroviral drug therapy, which…
In this article, we consider an HIV/AIDS epidemic model with four classes of individuals. We have discussed about basic properties of the system and found the basic reproduction number $R_0$ of the system. The stability analysis of the…
Recently, a long-term model of HIV infection dynamics was developed to describe the entire time course of the disease. It consists of a large system of ODEs with many parameters, and is expensive to simulate. In the current paper, this…
Oxidative stress, a reaction caused by the imbalance between the reactive oxygen species of human organism and its ability to detoxify reactive intermediates and to repair the resulting damage plays an important role in HIV-infections. On…
Objective: The reservoir of human immunodeficiency virus (HIV) latently infected cells is the major obstacle for eradication of acquired immunodeficiency syndrome (AIDS). Due to the noisy environment and multiple influencing factors in the…
In this paper, a mathematical analysis of the global dynamics of a partial differential equation viral infection cellular model is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both…
The search to understand how the HIV virus spreads inside the human body and how the immune response works to control it has motivated studies related to Mathematical Immunology. Actually, researches include the idea of mathematical models…
This contribution is devoted to a new model of HIV multiplication motivated by the patent of one of the authors. We take into account the antigenic diversity through what we define "antigenicity", whether of the virus or of the adapted…