scholarly journals An Allee Threshold Model for a Glioblastoma(GB)-Immune System(IS) Interaction with Fuzzy Initial Values

2019 ◽  
Vol 5 (1) ◽  
pp. 499-508
Author(s):  
Fatma Berna Benli ◽  
Onur Alp İlhan ◽  
Özgür Keskin
Keyword(s):  
Brain Tumor ◽  
Immune System ◽  
Numerical Simulations ◽  
Threshold Model ◽  
Initial Values

AbstractIn this paper, we adopt the model of [12] by including fuzzy initial values to study the interaction of a monoclonal brain tumor and the macrophages for a condition of extinction of GB(Glioblastoma) by using Allee threshold. Numerical simulations will give detailed information on the behavior of the model at the end of the paper. We perform all the computations in this study with the help of the Maple software.

Hyperstimulation of the immune system as a cause of autoimmune diseases

2020 ◽  
Vol 75 (3) ◽  
pp. 204-213
Author(s):  
Varvara A. Ryabkova ◽  
Leonid P. Churilov ◽  
Yehuda Shoenfeld
Keyword(s):  
Immune System ◽  
Autoimmune Diseases ◽  
Genetic Basis ◽  
Threshold Model ◽  
Subsequent Development ◽  
Threshold Effect ◽  
Successful Management ◽  
Polygenic Inheritance ◽  
Autoimmune Pathology ◽  
The Common

The pathogenesis of autoimmune diseases is very complex and multi-factorial. The concept of Mosaics of Autoimmunity was introduced to the scientific community 30 years ago by Y. Shoenfeld and D.A. Isenberg, and since then new tiles to the puzzle are continuously added. This concept specifies general pathological ideas about the multifactorial threshold model for polygenic inheritance with a threshold effect by the action of a number of external causal factors as applied to the field of autoimmunology. Among the external factors that can excessively stimulate the immune system, contributing to the development of autoimmune reactions, researchers are particularly interested in chemical substances, which are widely used in pharmacology and medicine. In this review we highlight the autoimmune dynamics i.e. a multistep pathogenesis of autoimmune diseases and the subsequent development of lymphoma in some cases. In this context several issues are addressed namely, genetic basis of autoimmunity; environmental immunostimulatory risk factors; gene/environmental interaction; pre-clinical autoimmunity with the presence of autoantibodies; and the mechanisms, underlying lymphomagenesis in autoimmune pathology. We believe that understanding the common model of the pathogenesis of autoimmune diseases is the first step to their successful management.

Heteroclinic Trajectory and Hopf Bifurcation in an Extended Lorenz System

2018 ◽  
Vol 28 (09) ◽  
pp. 1850111
Author(s):  
Xianyi Li ◽  
Haijun Wang
Keyword(s):  
Hopf Bifurcation ◽  
Lyapunov Function ◽  
Numerical Simulations ◽  
Lorenz System ◽  
The Other ◽  
Hopf Bifurcations ◽  
Limit Sets ◽  
Initial Values ◽  
Heteroclinic Trajectory ◽  
The One

This note revisits an extended Lorenz system, which was presented in the paper entitled “Hopf bifurcations in an extended Lorenz system” by Zhou et al. [2017]. On the one hand, one points out and corrects some wrong results in that paper on the Hopf bifurcation at the symmetric equilibria [Formula: see text] and [Formula: see text]. On the other hand, combining Lyapunov function and the concepts of [Formula: see text]- and [Formula: see text]-limit sets, it is rigorously proved that there exists two and only two heteroclinic trajectories but no homoclinic trajectories under some certain conditions of its parameters and initial values. In addition, numerical simulations illustrate the consistence with the theoretical conclusions. The results together not only improve and complement the known ones, but also provide support in some future applications.

INTERLEUKIN MATHEMATICAL MODEL OF AN IMMUNE SYSTEM

1995 ◽  
Vol 03 (03) ◽  
pp. 889-902 ◽  
Author(s):  
URSULA FORYS
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Immune System ◽  
Numerical Simulations ◽  
Basic Properties

Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.

scholarly journals The Pathophysiology of Post-Traumatic Glioma

2018 ◽  
Vol 19 (8) ◽  
pp. 2445 ◽  
Author(s):  
Donata Simińska ◽  
Klaudyna Kojder ◽  
Dariusz Jeżewski ◽  
Ireneusz Kojder ◽  
Marta Skórka ◽  
...  
Keyword(s):  
Brain Tumor ◽  
Immune System ◽  
Experimental Studies ◽  
Epidemiological Studies ◽  
Detection Rates ◽  
Expression Of Genes ◽  
Specific Morphology ◽  
Post Traumatic ◽  
The Brain ◽  
Very High

Malignant glioma is a brain tumor with a very high mortality rate resulting from the specific morphology of its infiltrative growth and poor early detection rates. The causes of one of its very specific types, i.e., post-traumatic glioma, have been discussed for many years, with some studies providing evidence for mechanisms where the reaction to an injury may in some cases lead to the onset of carcinogenesis in the brain. In this review of the available literature, we discuss the consequences of breaking the blood–brain barrier and consequences of the influx of immune-system cells to the site of injury. We also analyze the influence of inflammatory mediators on the expression of genes controlling the process of apoptosis and the effect of chemical mutagenic factors on glial cells in the brain. We present the results of experimental studies indicating a relationship between injury and glioma development. However, epidemiological studies on post-traumatic glioma, of which only a few confirm the conclusions of experimental research, indicate that any potential relationship between injury and glioma, if any, is indirect.

scholarly journals Numerical Simulations of a Delay Model for Immune System-Tumor Interaction

2018 ◽  
Vol 23 (1) ◽  
pp. 19 ◽  
Author(s):  
Mohamed A. Hajji ◽  
Qasem Al-Mdallal
Keyword(s):  
Steady State ◽  
Immune System ◽  
Numerical Simulations ◽  
Relative Rate ◽  
Delay Model ◽  
Effector Cells ◽  
Rate Of Increase ◽  
System Tumor ◽  
Delay Differential ◽  
Parameter Values

In this paper we consider a system of delay differential equations as a model for the dynamics of tumor-immune system interaction. We carry out a stability analysis of the proposed model. In particular, we show that the system can have up to two steady states: the tumor free steady state, which always exist, and the tumor persistent steady state, which exists only when the relative rate of increase of the tumor cells exceeds the ratio between the natural proliferation rate and the relative death rate of the effector cells. We also determine an upper bound for the delay, such that stability is preserved. Numerical simulations of the system under different parameter values are performed.

scholarly journals Abstract 977: Nano immunotherapeutics crossing blood-brain barrier to activate local brain tumor immune system

2019 ◽  
Author(s):  
Anna Galstyan ◽  
Antonella Chiechi ◽  
Tao Sun ◽  
Ekaterina S. Shatalova ◽  
Rameshwar Patil ◽  
...  
Keyword(s):  
Brain Tumor ◽  
Immune System ◽  
Blood Brain Barrier ◽  
Brain Barrier ◽  
Blood Brain ◽  
Local Brain

scholarly journals Perturbation Maps and the ring of Haumea

2020 ◽  
Vol 496 (2) ◽  
pp. 2085-2097
Author(s):  
Diogo M Sanchez ◽  
Rogerio Deienno ◽  
Antonio F B A Prado ◽  
Kathleen C Howell
Keyword(s):  
Numerical Simulations ◽  
Orbital Motion ◽  
Stable Region ◽  
Integral Type ◽  
Initial Angle ◽  
Initial Values ◽  
Single Ring ◽  
Perturbation Maps

ABSTRACT The dwarf planet Haumea is a trans-Neptunian object that is orbited by two moons and has a recently discovered ring. The particles of this ring are near the 3:1 resonance between the spin of Haumea and the orbital motion of the particles. In this work, the ring of Haumea is investigated using Perturbation Maps. These maps show the behaviour and impact of perturbations acting over particles around Haumea. The information coming from the maps depends on the integral type for the disturbing acceleration used to build the maps. The types II and IV are used. The numerical simulations are focused in the region between 2000 and 2500 km from the centre of Haumea, which is the region where the ring was observed, considering two initial values for the 3:1 resonant angle: θres = 0° and θres = 270°. The possible stable region for the initial angle θres = 0° is larger than the stable region for the initial angle θres = 270°. Furthermore, we found that these stable regions are not continuous, indicating that there are possible gaps in the ring. Therefore, our results suggest that Haumea may not have only one single ring, but a system of rings instead. Possible transit of the particles between the ring and the region close to the orbit of Namaka is also shown.

scholarly journals Leapfrogging of electrical solitons in coupled nonlinear transmission lines: effect of an imperfect varactor

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Nkongho Achere Akem ◽  
Alain M. Dikandé ◽  
B. Z. Essimbi
Keyword(s):  
Harmonic Oscillator ◽  
Transmission Line ◽  
Numerical Simulations ◽  
Transmission Lines ◽  
Nonlinear Transmission Lines ◽  
Capacitively Coupled ◽  
Nonlinear Transmission ◽  
Damped Harmonic Oscillator ◽  
Initial Values ◽  
Soliton Pair

AbstractThe leapfrogging dynamics of a pair of electrical solitons is investigated, by considering two capacitively coupled nonlinear transmission lines with and without intraline resistances. We discuss two distinct transmission line set-ups: in the first, we assume two RLC ladder lines with intraline varactors and a coupling linear capacitor, and in the second, we consider two capacitively coupled lossless lines with a varactor carrying impurity (imperfect diode) in one of the two interacting transmission lines. In the first context, we find that the soliton-pair leapfrogging mimics the motion of a damped harmonic oscillator, the frequency and damping coefficient of which are obtained analytically. Numerical simulations predict leapfrogging of the soliton pair when the differences in the initial values of the amplitude and phase are reasonably small, and the resistance is not too large. In the second context, leapfrogging occurs when the impurity rate is small enough and the differences in the initial values of the amplitude as well as phase are also small. As the impurity rate increases, the soliton signal in the imperfect line gets accelerated upon approaching the defective diode, causing only this specific soliton signal to move faster than its counterpart, leading to the suppression of leapfrogging.

Sign in / Sign up

Export Citation Format

Share Document