Related papers: Stability of a viral infection model with state-de…
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…
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…
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,…
In this paper, we propose a delayed cytokine-enhanced viral infection model incorporating saturation incidence and immune response. We compute the basic reproduction numbers and introduce a convex cone to discuss the impact of non-negative…
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…
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…
We study the global stability of a class of models for in-vivo virus dynamics, that take into account the CTL immune response and display antigenic variation. This class includes a number of models that have been extensively used to model…
A retrovirus dynamic model is proposed. We pay attention to the case when viral pathogenicity is low and the infected cells are able to reproduce. Using Lyapunov function method we study stability properties of an inner equilibrium of the…
We consider a model of antiviral immune response proposed in the works of G.I. Marchuk. The model is described by a system of delay differential equations. The asymptotic stability of a stationary solution to the system corresponding to a…
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…
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 this paper, we develop a dynamic model of HIV infection that incorporates latent hosts, cytotoxic T lymphocyte (CTL) immunity, saturated incidence rates, and two transmission mechanisms: virus-to-cell and cell-to-cell transmission. The…
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 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,…
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 the theoretical research of Hepatitis B virus, mathematical models of its transmission mechanism have been thoroughly investigated, while the dynamics of the immune process in vivo have not. At present, nearly all the existing models are…
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…
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…
Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which…
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…