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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…
The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations…
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,…
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…
The rates of escape and reversion in response to selection pressure arising from the host immune system, notably the cytotoxic T-lymphocyte (CTL) response, are key factors determining the evolution of HIV. Existing methods for estimating…
Bacteria and their viruses ("bacteriophages") coexist in natural environments forming complex infection networks. Recent empirical findings suggest that phage-bacteria infection networks often possess a nested structure such that there is a…
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…
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…
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…
The vertebrate adaptive immune system provides a flexible and diverse set of molecules to neutralize pathogens. Yet, viruses such as HIV can cause chronic infections by evolving as quickly as the adaptive immune system, forming an…
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…
Human immunodeficiency virus (HIV-1 or simply HIV) induces a persistent infection, which in the absence of treatment leads to AIDS and death in almost all infected individuals. HIV infection elicits a vigorous immune response starting about…
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…
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…
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…
The coexistence of different viral strains (quasispecies) within the same host are nowadays observed for a growing number of viruses, most notably HIV, Marburg and Ebola, but the conditions for the formation and survival of new strains have…
Inspired by DNA data of the human cytomegalovirus we propose a model of a two-type parasite population distributed over its hosts. The parasite is capable to persist in its host till the host dies, and to reinfect other hosts. To maintain…
A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a…
This paper describes a novel approach to modeling homphily, i.e. the tendency of nodes that share (or differ in) certain attributes to be linked; we consider dynamic networks in which nodes can be added over time but not removed. Our…
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…