Related papers: A cytokine-enhanced viral infection model with CTL…
In this paper, we discussed an infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and…
In [Math. Comput. Sci. 12 (2018), no. 2, 111--127], a delayed model describing the dynamics of the Human Immunodeficiency Virus (HIV) with Cytotoxic T Lymphocytes (CTL) immune response is investigated by Allali, Harroudi and Torres. Here,…
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…
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…
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 delayed model describing the dynamics of HIV (Human Immunodeficiency Virus) with CTL (Cytotoxic T Lymphocytes) immune response is investigated. The model includes four nonlinear differential equations describing the evolution of…
A class of reaction-diffusion virus dynamics models with intracellular state-dependent delay and a general non-linear infection rate functional response is investigated. We are interested in classical solutions with Lipschitz in-time…
We analyze a within-host model of virus infection with antibody and CD8+ cytotoxic T lymphocyte (CTL) responses proposed by Schwartz et al. (2013). The goal of this work is to gain an overview of the stability of the biologically-relevant…
When an infectious disease propagates throughout society, the incidence function may rise at first due to an increase in pathogenicity and then decrease due to inhibitory effects until it reaches saturation. Effective vaccination and…
In this chapter, we consider a reaction-diffusion SVIR infection model with dis-tributed delay and nonlinear incidence rate. The wellposedness of the proposed model is proved. By means of Lyapunov functionals, we show that the disease-free…
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…
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…
We propose and investigate a delayed model that studies the relationship between HIV and the immune system during the natural course of infection and in the context of antiviral treatment regimes. Sufficient criteria for local asymptotic…
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,…
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…
The aims of this work is to analyse of the global stability of the extended model of hepatitis C virus(HCV) infection with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We first give general information about…
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…
Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. Recent mathematical models are aimed at studying dynamics of some specific types of infectious diseases. In…
We investigate an infection-age structured competitive epidemiological model involving multiple strains. While classical results establish competitive exclusion when a unique maximal basic reproduction number exists, we provide here a…