Global dynamics of cell mediated immunity in viral infection models with distributed delays

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 and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection $R_{0}$ and for CTL response $R_{1}$ such that $R_{1}<R_{0}$. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if $R_{0}\leq1$, an infected equilibrium without immune response is globally asymptotically stable if $R_{1}\leq1<R_{0}$ and an infected equilibrium with immune response is globally asymptotically stable if $R_{1}>1$. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if $R_{1}>1$.Comment: 16 pages, accepted by Journal of Mathematical Analysis and Application

A continuous strain-space model of viral evolution within a host

Viruses rapidly evolve, and HIV in particular is known to be one of the fastest evolving human viruses. It is now commonly accepted that viral evolution is the cause of the intriguing dynamics exhibited during HIV infections and the ultimate success of the virus in its struggle with the immune system. To study viral evolution, we use a simple mathematical model of the within-host dynamics of HIV which incorporates random mutations. In this model, we assume a continuous distribution of viral strains in a one-dimensional phenotype space where random mutations are modelled by di ffusion. Numerical simulations show that random mutations combined with competition result in evolution towards higher Darwinian fitness: a stable traveling wave of evolution, moving towards higher levels of fi tness, is formed in the phenoty space

Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response

Virus dynamics models are useful in interpreting and predicting the change in viral load over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B virus (HBV).We propose a mathematical model involving the role of total immune response (innate, CTL, and humoral) and treatment for productively infected cells and free virus to understand the dynamics of virus–host interactions. A threshold condition for the extinction or persistence of infection, i.e. basic reproductive number, in the presence of immune response (RI ) is established. We study the global stability of virus-free equilibrium and interior equilibrium using LaSalle’s principle and Lyapunov’s direct method. The global stability of virus-free equilibrium ensures the clearance of virus from the body, which is independent of initial status of subpopulations. Central manifold theory is used to study the behavior of equilibrium points at RI = 1, i.e. when the basic reproductive number in the presence of immune response is one. A special case, when the immune response (IR) is not present, has also been discussed. Analysis of special case suggests that the basic reproductive number in the absence of immune response R0 is greater than that of in the presence of immune response RI , i.e. R0&gt; RI . It indicates that infection may be eradicated if RI &nbsp;&lt; 1. Numerical simulations are performed to illustrate the analytical results using MatLab and Mathematica

Egress of non-enveloped enteric RNA viruses

A long-standing paradigm in virology was that non-enveloped viruses induce cell lysis to release progeny virions. However, emerging evidence indicates that some non-enveloped viruses exit cells without inducing cell lysis, while others engage both lytic and non-lytic egress mechanisms. Enteric viruses are transmitted via the faecal-oral route and are important causes of a wide range of human infections, both gastrointestinal and extra-intestinal. Virus cellular egress, when fully understood, may be a relevant target for antiviral therapies, which could minimize the public health impact of these infections. In this review, we outline lytic and non-lytic cell egress mechanisms of non-enveloped enteric RNA viruses belonging to five families: Picornaviridae, Reoviridae, Caliciviridae, Astroviridae and Hepeviridae. We discuss factors that contribute to egress mechanisms and the relevance of these mechanisms to virion stability, infectivity and transmission. Since most data were obtained in traditional two-dimensional cell cultures, we will further attempt to place them into the context of polarized cultures and in vivo pathogenesis. Throughout the review, we highlight numerous knowledge gaps to stimulate future research into the egress mechanisms of these highly prevalent but largely understudied viruses

Stability of a mathematical model of tumour-induced angiogenesis

A model consisting of three differential equations to simulate the interactions between cancer cells, the angiogenic factors and endothelial progenitor cells in tumor growth is developed. Firstly, the global existence, nonnegativity and boundedness of the solutions are discussed. Secondly, by analyzing the corresponding characteristic equations, the local stability of three boundary equilibria and the angiogenesis equilibrium of the model is discussed, respectively. We further consider global asymptotic stability of the boundary equilibria and the angiogenesis equilibrium by using the well-known Liapunov–LaSalle invariance principal. Finally, some numerical simulations are given to support the theoretical results

Effect of Time Delay on Spatial Patterns in a Airal Infection Model with Diffusion

This paper is concerned with the dynamics of a viral infection model with diffusion under the assumption that the immune response is retarded. A time delay is incorporated into the model described the delayed immune response after viral infection. Based upon a stability analysis, we demonstrate that the appearance, or the absence, of spatial patterns is determined by the delay under some conditions. Moreover, the spatial patterns occurs as a consequence of Hopf bifurcation. By applying the normal form and the center manifold theory, the direction as well as the stability of the Hopf bifurcation is explored. In addition, a series of numerical simulations are performed to illustrate our theoretical results

Exploration of a novel non-lytic viral transmission mechanism utilized by a non-enveloped positive-sense RNA virus

While enteroviruses, including poliovirus, are conventionally released upon cell lysis, recent studies show that phosphatidylserine-enriched infectious extracellular vesicles (IEVs) shed by infected cells can transport clusters of enteroviruses from cell to cell, resulting in increased infectivity. Combining structural and biochemical analyses, we focused on IEVs shed from poliovirus-infected cells, a classical prototype for studying enteroviruses. Transmission cryo-electron microscopy, cryo-electron tomography and computational reconstruction, present the first three-dimensional structures of well-preserved IEVs and purified exosomes. We observed that single-membraned IEVs present a wide size range in diameter. Clusters of virions can be either densely packed within a protein-coated irregularly shaped IEV, or concentrated at one or both ends of an IEV, forming a polar structure. In addition to virions, IEVs often contain internal vesicles, “ramen-noodle”-like structures with strong density, and partially assembled virion-like structures. Viral replication complex components, including viral proteins polymerase 3D, 3CD, 3A, 3AB, 2BC, 2C and (+) and (-) stranded RNAs were detected in IEVs. Furthermore, (-) stranded RNA templates are protected by the IEVs, not packed in viral capsids. The transported viral replication components (viral proteins and RNAs) and virions within IEVs initiate a stronger and faster viral replication in recipient cells than free virions. Both cryo-electron tomographic and mass spectrometry data also showed that virions and “ramen-noodle”-like structures were also observed in purified CD9 positive exosomes from poliovirus-infected cells. Viral protein 3AB, detected on the membrane of IEVs, can invaginate membranous structures to engulf large proteins into a closed lumen. Our study demonstrates that IEVs can transport viral replication complex components to initiate a rapid onset of viral replication, as part of a novel viral transmission mechanism. Viral protein 3AB may contribute to forming IEVs throughout the infection.2019-06-12T00:00:00