scholarly journals The effect of time delay and Hopf bifurcation in a tumor-immune system competition model with negative immune response

2009 ◽  
Vol 36 (3) ◽  
pp. 349-364
Author(s):  
Radouane Yafia
Keyword(s):  
Immune Response ◽  
Immune System ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Competition Model

scholarly journals Hopf bifurcation in a delayed model for tumor-immune system competition with negative immune response

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
Radouane Yafia
Keyword(s):  
Immune Response ◽  
Asymptotic Behavior ◽  
Steady State ◽  
Immune System ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Limit Cycle ◽  
Numerical Study ◽  
Bifurcation Problem ◽  
Delayed Model

The dynamics of the model for tumor-immune system competition with negative immune response and with one delay investigated. We show that the asymptotic behavior depends crucially on the time delay parameter. We are particularly interested in the study of the Hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state, by using the delay as a parameter of bifurcation. The obtained results provide the oscillations given by the numerical study in M. Gałach (2003), which are observed in reality by Kirschner and Panetta (1998).

scholarly journals EFFECT OF TIME DELAY ON SPATIAL PATTERNS IN A AIRAL INFECTION MODEL WITH DIFFUSION

2016 ◽  
Vol 21 (2) ◽  
pp. 143-158
Author(s):  
Jia Liu ◽  
Qunying Zhang ◽  
Canrong Tian
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Viral Infection ◽  
Spatial Patterns ◽  
Infection Model ◽  
The Stability ◽  
Manifold Theory ◽  
Viral Infection Model ◽  
Theoretical Results

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.

scholarly journals Stability of limit cycle in a delayed model for tumor immune system competition with negative immune response

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
Radouane Yafia
Keyword(s):  
Immune Response ◽  
Immune System ◽  
Hopf Bifurcation ◽  
Discrete Delay ◽  
Local Asymptotic Stability ◽  
Nonlinear Delay Differential Equations ◽  
The Stability ◽  
Delay Differential ◽  
Delayed Model ◽  
Nonlinear Delay

This paper is devoted to the study of the stability of limit cycles of a system of nonlinear delay differential equations with a discrete delay. The system arises from a model of population dynamics describing the competition between tumor and immune system with negative immune response. We study the local asymptotic stability of the unique nontrivial equilibrium of the delay equation and we show that its stability can be lost through a Hopf bifurcation. We establish an explicit algorithm for determining the direction of the Hopf bifurcation and the stability or instability of the bifurcating branch of periodic solutions, using the methods presented by Diekmann et al.

Numerical Approximation of Hopf Bifurcation for Tumor-Immune System Competition Model with Two Delays

2013 ◽  
Vol 5 (2) ◽  
pp. 146-162
Author(s):  
Jing-Jun Zhao ◽  
Jing-Yu Xiao ◽  
Yang Xu
Keyword(s):  
Immune System ◽  
Hopf Bifurcation ◽  
Numerical Approximation ◽  
Center Manifold ◽  
Competition Model ◽  
Center Manifold Theory ◽  
Two Delays ◽  
Normal Form Method ◽  
The Stability ◽  
Manifold Theory

AbstractThis paper is concerned with the Hopf bifurcation analysis of tumor-immune system competition model with two delays. First, we discuss the stability of state points with different kinds of delays. Then, a sufficient condition to the existence of the Hopf bifurcation is derived with parameters at different points. Furthermore, under this condition, the stability and direction of bifurcation are determined by applying the normal form method and the center manifold theory. Finally, a kind of Runge-Kutta methods is given out to simulate the periodic solutions numerically. At last, some numerical experiments are given to match well with the main conclusion of this paper.

scholarly journals Equivariant Hopf Bifurcation in a Time-Delayed Ring of Antigenic Variants

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Israel Ncube
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Antigenic Variation ◽  
Single Species ◽  
Endemic Equilibrium ◽  
Equivariant Hopf Bifurcation ◽  
Bifurcation And Stability ◽  
Malaria Model

We consider an intrahost malaria model allowing for antigenic variation within a single species. The host’s immune response is compartmentalised into reactions to major and minor epitopes. We investigate the dynamics of the model, paying particular attention to bifurcation and stability of the uniform nonzero endemic equilibrium. We establish conditions for the existence of an equivariant Hopf bifurcation in a ring of antigenic variants, characterised by time delay.

scholarly journals Secondary haemophagocytic lymphohistiocytosis in COVID-19: correlation of the autopsy findings of bone marrow haemophagocytosis with HScore

2021 ◽  
pp. jclinpath-2020-207337
Author(s):  
Claudia Núñez-Torrón ◽  
Ana Ferrer-Gómez ◽  
Esther Moreno Moreno ◽  
Belen Pérez-Mies ◽  
Jesús Villarrubia ◽  
...  
Keyword(s):  
Bone Marrow ◽  
Immune Response ◽  
Immune System ◽  
Multiorgan Failure ◽  
Histological Findings ◽  
Haemophagocytic Lymphohistiocytosis ◽  
Bone Marrow Tissue ◽  
Autopsy Findings ◽  
Specific Finding ◽  
Clinical Records

BackgroundSecondary haemophagocytic lymphohistiocytosis (sHLH) is characterised by a hyper activation of immune system that leads to multiorgan failure. It is suggested that excessive immune response in patients with COVID-19 could mimic this syndrome. Some COVID-19 autopsy studies have revealed the presence of haemophagocytosis images in bone marrow, raising the possibility, along with HScore parameters, of sHLH.AimOur objective is to ascertain the existence of sHLH in some patients with severe COVID-19.MethodsWe report the autopsy histological findings of 16 patients with COVID-19, focusing on the presence of haemophagocytosis in bone marrow, obtained from rib squeeze and integrating these findings with HScore parameters. CD68 immunohistochemical stains were used to highlight histiocytes and haemophagocytic cells. Clinical evolution and laboratory parameters of patients were collected from electronic clinical records.ResultsEleven patients (68.7%) displayed moderate histiocytic hyperplasia with haemophagocytosis (HHH) in bone marrow, three patients (18.7%) displayed severe HHH and the remainder were mild. All HScore parameters were collected in 10 patients (62.5%). Among the patients in which all parameters were evaluable, eight patients (80%) had an HScore >169. sHLH was not clinically suspected in any case.ConclusionsOur results support the recommendation of some authors to use the HScore in patients with severe COVID-19 in order to identify those who could benefit from immunosuppressive therapies. The presence of haemophagocytosis in bone marrow tissue, despite not being a specific finding, has proved to be a very useful tool in our study to identify these patients.

scholarly journals The immune response of T cells and therapeutic targets related to regulating the levels of T helper cells after ischaemic stroke

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Tian-Yu Lei ◽  
Ying-Ze Ye ◽  
Xi-Qun Zhu ◽  
Daniel Smerin ◽  
Li-Juan Gu ◽  
...  
Keyword(s):  
Immune Response ◽  
T Cells ◽  
Immune System ◽  
Immune Responses ◽  
Ischaemic Stroke ◽  
Immune Cells ◽  
Tissue Injury ◽  
Recovery Period ◽  
Vital Functions ◽  
Anti Inflammatory

AbstractThrough considerable effort in research and clinical studies, the immune system has been identified as a participant in the onset and progression of brain injury after ischaemic stroke. Due to the involvement of all types of immune cells, the roles of the immune system in stroke pathology and associated effects are complicated. Past research concentrated on the functions of monocytes and neutrophils in the pathogenesis of ischaemic stroke and tried to demonstrate the mechanisms of tissue injury and protection involving these immune cells. Within the past several years, an increasing number of studies have elucidated the vital functions of T cells in the innate and adaptive immune responses in both the acute and chronic phases of ischaemic stroke. Recently, the phenotypes of T cells with proinflammatory or anti-inflammatory function have been demonstrated in detail. T cells with distinctive phenotypes can also influence cerebral inflammation through various pathways, such as regulating the immune response, interacting with brain-resident immune cells and modulating neurogenesis and angiogenesis during different phases following stroke. In view of the limited treatment options available following stroke other than tissue plasminogen activator therapy, understanding the function of immune responses, especially T cell responses, in the post-stroke recovery period can provide a new therapeutic direction. Here, we discuss the different functions and temporal evolution of T cells with different phenotypes during the acute and chronic phases of ischaemic stroke. We suggest that modulating the balance between the proinflammatory and anti-inflammatory functions of T cells with distinct phenotypes may become a potential therapeutic approach that reduces the mortality and improves the functional outcomes and prognosis of patients suffering from ischaemic stroke.

scholarly journals Why Does SARS-CoV-2 Infection Induce Autoantibody Production?

Pathogens ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 380
Author(s):  
Ales Macela ◽  
Klara Kubelkova
Keyword(s):  
Immune Response ◽  
Immune System ◽  
Host Cell ◽  
Critical Role ◽  
Cell Interaction ◽  
Immune Recognition ◽  
Autoantibody Production ◽  
Host Cell Interaction ◽  
Primary Virus

SARS-CoV-2 infection induces the production of autoantibodies, which is significantly associated with complications during hospitalization and a more severe prognosis in COVID-19 patients. Such a response of the patient’s immune system may reflect (1) the dysregulation of the immune response or (2) it may be an attempt to regulate itself in situations where the non-infectious self poses a greater threat than the infectious non-self. Of significance may be the primary virus-host cell interaction where the surface-bound ACE2 ectoenzyme plays a critical role. Here, we present a brief analysis of recent findings concerning the immune recognition of SARS-CoV-2, which, we believe, favors the second possibility as the underlying reason for the production of autoantibodies during COVID-19.

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