Related papers: Stability and Optimal Control of a Delayed HIV Mod…
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…
Combination Antiretroviral Therapy (cART) succeeds to control viral replication in most HIV infected patients. This is normally followed by a reconstitution of the CD4$^+$ T cells pool; however, this does not happen for a substantial…
In this paper we present a delay induced model for hepatitis C virus incorporating the healthy and infected hepatocytes as well as infectious and noninfectious virions. The model is mathematically analyzed and characterized, both for the…
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 paper we study a model of HCV with mitotic proliferation, a saturation infection rate and a discrete intracellular delay: the delay corresponds to the time between infection of a infected target hepatocytes and production of new HCV…
We consider a recent coinfection model for Tuberculosis (TB), Human Immunodeficiency Virus (HIV) infection and Acquired Immunodeficiency Syndrome (AIDS) proposed in [Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639--4663]. We introduce…
This paper is about numerical control of HIV propagation. The contribution of the paper is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the…
This paper introduces a new optimal control model to describe and control the dynamics of infectious diseases. In the present model, the average time of isolation (i.e. hospitalization) of infectious population is the main time-dependent…
A major contribution to the onset and development of autoimmune disease is known to come from infections. An important practical problem is identifying the precise mechanism by which the breakdown of immune tolerance as a result of immune…
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…
The aim of this work is to make a survey on recent sufficient optimality conditions for optimal control problems with time delays in both state and control variables. The results are obtained by transforming delayed optimal control problems…
Pre-exposure prophylaxis (PrEP) consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals and has recently demonstrated to be highly efficacious for HIV prevention. We propose…
For centuries isolation has been the main control strategy of unforeseen epidemic outbreaks. When implemented in full and without delay, isolation is very effective. However, flawless implementation is seldom feasible in practice. We…
A virus dynamics model with intracellular state-dependent delay and nonlinear infection rate of Beddington-DeAngelis functional response is studied. The technique of Lyapunov functionals is used to analyze stability of an interior infection…
Tuberculosis (TB) and human immunodeficiency virus (HIV) can be considered a deadly human syndemic. In this article, we formulate a model for TB and HIV transmission dynamics. The model considers both TB and acquired immune deficiency…
In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in \textit{vivo}. The model has two distributed time delays describing time needed for infection of cell…
Case isolation, that is, detection and isolation of infected individuals in order to prevent spread, is a strategy to curb infectious disease epidemics. Here, we study the efficiency of a case isolation strategy subject to time delays in…
We consider a time-delayed HIV/AIDS epidemic model with education dissemination and study the asymptotic dynamics of solutions as well as the asymptotic behavior of the endemic equilibrium with respect to the amount of information…
In this paper we consider a delayed nonlinear model of the dynamics of the immune system against a viral infection that contains wild-type virus and one mutant. A finite response time of the immune system was considered in order which leads…
In this research, we have derived a mathematical model for within human dynamics of COVID-19 infection using delay differential equations. The new model considers a 'latent period' and 'the time for immune response' as delay parameters,…