scholarly journals Spatiotemporal dynamics of a glioma immune interaction model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Subhas Khajanchi ◽  
Juan J. Nieto
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
T Lymphocytes ◽  
Numerical Simulations ◽  
Cytotoxic T Lymphocytes ◽  
Cell Population ◽  
Glioma Cell ◽  
Interaction Model ◽  
Spatiotemporal Dynamics ◽  
Reaction Diffusion Equations

AbstractWe report a mathematical model which depicts the spatiotemporal dynamics of glioma cells, macrophages, cytotoxic-T-lymphocytes, immuno-suppressive cytokine TGF-β and immuno-stimulatory cytokine IFN-γ through a system of five coupled reaction-diffusion equations. We performed local stability analysis of the biologically based mathematical model for the growth of glioma cell population and their environment. The presented stability analysis of the model system demonstrates that the temporally stable positive interior steady state remains stable under the small inhomogeneous spatiotemporal perturbations. The irregular spatiotemporal dynamics of gliomas, macrophages and cytotoxic T-lymphocytes are discussed extensively and some numerical simulations are presented. Performed some numerical simulations in both one and two dimensional spaces. The occurrence of heterogeneous pattern formation of the system has both biological and mathematical implications and the concepts of glioma cell progression and invasion are considered. Simulation of the model shows that by increasing the value of time, the glioma cell population, macrophages and cytotoxic-T-lymphocytes spread throughout the domain.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

scholarly journals A Mathematical Model to Study the Effectiveness of Some of the Strategies Adopted in Curtailing the Spread of COVID-19

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Isa Abdullahi Baba ◽  
Bashir Abdullahi Baba ◽  
Parvaneh Esmaili
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Government Policy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Compartmental Models ◽  
Effective Strategy ◽  
Local Stability Analysis ◽  
The Government

In this paper, we developed a model that suggests the use of robots in identifying COVID-19-positive patients and which studied the effectiveness of the government policy of prohibiting migration of individuals into their countries especially from those countries that were known to have COVID-19 epidemic. Two compartmental models consisting of two equations each were constructed. The models studied the use of robots for the identification of COVID-19-positive patients. The effect of migration ban strategy was also studied. Four biologically meaningful equilibrium points were found. Their local stability analysis was also carried out. Numerical simulations were carried out, and the most effective strategy to curtail the spread of the disease was shown.

scholarly journals Large clonal expansions of human virus-specific memory cytotoxic T lymphocytes within the CD57+ CD28- CD8+ T-cell population

Immunology ◽  
1999 ◽  
Vol 98 (3) ◽  
pp. 443-449 ◽  
Author(s):  
M. P. Weekes ◽  
M. R. Wills ◽  
K. Mynard ◽  
R. Hicks ◽  
J. G. P. Sissons ◽  
...  
Keyword(s):  
T Cell ◽  
T Lymphocytes ◽  
Cytotoxic T Lymphocytes ◽  
Cell Population ◽  
Cd8 T Cell ◽  
Human Virus ◽  
Specific Memory ◽  
Memory Cytotoxic T Lymphocytes

Spread of Tuberculosis Among Smokers

2020 ◽  
pp. 49-73
Author(s):  
Purvi M. Pandya ◽  
Ekta N. Jayswal ◽  
Yash Shah
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Psychological Health ◽  
Matrix Method ◽  
Equilibrium Points ◽  
Research Work ◽  
Linear Ordinary Differential Equations ◽  
Smoking Addiction ◽  
The Mathematical Model

Smoking tobacco has some hazardous implications on an individual's physical, physiological, and psychological health; health of the passive smokers near him or her; and on the surrounding environment. From carcinomas to auto-immune disorders, smoking has a role to play. Therefore, there arises a need to frame a systemic pathway to decipher relationship between smoking and a perilous disease such as tuberculosis. This research work focuses on how drugs or medications can affect individuals who are susceptible to tuberculosis because of smoking habits and also on individuals who have already developed symptoms of tuberculosis due to their smoking addiction. The mathematical model is formulated using non-linear ordinary differential equations, and then threshold is calculated for different equilibrium points using next generation matrix method. Stability analysis along with numerical simulations are carried out to validate the data.

Clonal analysis in the ultrastructure of cell-to-cell interaction between a human glioma cell line and autologous tumor-specific cytotoxic T lymphocytes

1990 ◽  
Vol 126 (1) ◽  
pp. 164-175 ◽  
Author(s):  
Kouichi Iwasaki ◽  
Haruhiko Kikuchi ◽  
Shin-ichi Miyatake ◽  
Yoshifumi Oda ◽  
Junkoh Yamashita ◽  
...  
Keyword(s):  
T Lymphocytes ◽  
Cell Line ◽  
Cytotoxic T Lymphocytes ◽  
Glioma Cell ◽  
Cell Interaction ◽  
Glioma Cell Line ◽  
Clonal Analysis ◽  
Autologous Tumor ◽  
Human Glioma ◽  
Human Glioma Cell

scholarly journals On the generalized fractional snap boundary problems via G-Caputo operators: existence and stability analysis

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammad Esmael Samei ◽  
Mohammed M. Matar ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Mathematical Model ◽  
Integral Equation ◽  
Fixed Point ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Boundary Problems ◽  
Existence And Stability ◽  
Existence Criterion ◽  
The Mathematical Model ◽  
Fixed Point Techniques

AbstractThis research is conducted for studying some qualitative specifications of solution to a generalized fractional structure of the standard snap boundary problem. We first rewrite the mathematical model of the extended fractional snap problem by means of the $\mathbb{G}$ G -operators. After finding its equivalent solution as a form of the integral equation, we establish the existence criterion of this reformulated model with respect to some known fixed point techniques. Then we analyze its stability and further investigate the inclusion version of the problem with the help of some special contractions. We present numerical simulations for solutions of several examples regarding the fractional $\mathbb{G}$ G -snap system in different structures including the Caputo, Caputo–Hadamard, and Katugampola operators of different orders.

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