Journal ArticleDOI
Stability and bifurcation analysis of delay induced tumor immune interaction model
Subhas Khajanchi,Sandip Banerjee +1 more
TLDR
A modified mathematical model of Kuznetsov et al. (1994) representing tumor-immune interaction with discrete time delay with bifurcation parameter is proposed, based on the normal form theory and center manifold theorem, to establish the sufficient condition for local stability of interior steady state.About:
This article is published in Applied Mathematics and Computation.The article was published on 2014-12-01. It has received 71 citations till now. The article focuses on the topics: Saddle-node bifurcation & Bifurcation diagram.read more
Citations
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Journal ArticleDOI
Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays
TL;DR: In this paper, the global exponential stability of quaternion-valued recurrent neural networks (QVNNs) with time-varying delays is investigated, where the activation functions are not assumed to be derivative any more, making the analytical procedure compact.
Journal ArticleDOI
Matrix measure method for global exponential stability of complex-valued recurrent neural networks with time-varying delays
TL;DR: In this paper, based on the matrix measure method and the Halanay inequality, the global exponential stability problem is investigated for the complex-valued recurrent neural networks with time-varying delays.
Journal ArticleDOI
The influence of time delay in a chaotic cancer model.
TL;DR: A mathematical model that describes how tumor cells evolve and survive the brief encounter with the immune system, mediated by effector cells and host cells is presented and it is shown that the delayed model exhibits periodic oscillations as well as chaotic behavior, which are often indicators of long-term tumor relapse.
Journal ArticleDOI
Mathematical modeling of tumor-immune cell interactions.
TL;DR: This succinct review offers an overview of recent tumor-immune continuum modeling approaches, highlighting spatial models and incorporating one or more immune cell types and evaluating immune cell effects on tumor progression.
Journal ArticleDOI
Multistability of complex-valued neural networks with discontinuous activation functions.
TL;DR: Based on the geometrical properties of the discontinuous activation functions and the Brouwer's fixed point theory, the multistability issue is tackled for the complex-valued neural networks with discontinuousactivation functions and time-varying delays.
References
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Book
Introduction to Applied Nonlinear Dynamical Systems and Chaos
TL;DR: The Poincare-Bendixson Theorem as mentioned in this paper describes the existence, uniqueness, differentiability, and flow properties of vector fields, and is used to prove that a dynamical system is Chaotic.
Journal ArticleDOI
Treatment of 283 Consecutive Patients With Metastatic Melanoma or Renal Cell Cancer Using High-Dose Bolus Interleukin 2
Steven A. Rosenberg,James Chih-Hsin Yang,Suzanne L. Topalian,Douglas J. Schwartzentruber,Jeffrey S. Weber,David R. Parkinson,Claudia A. Seipp,Jan Einhorn,Donald E. White +8 more
TL;DR: Because IL-2 does not have a direct effect on cancer cells but rather mediates its antitumor activity by altering host immune reactions, these data represent the best available evidence that immunologic therapy for cancer can be effective in selected patients.
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Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis
TL;DR: The model exhibits a number of phenomena that are seen in vivo, including immunostimulation of tumor growth, "sneaking through" of the tumor, and formation of a tumor "dormant state".
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Modeling immunotherapy of the tumor-immune interaction.
TL;DR: The dynamics between tumor cells, immune-effector cells, and IL-2 are illustrated through mathematical modeling and the effects of adoptive cellular immunotherapy are explored to explain both short tumor oscillations in tumor sizes as well as long-term tumor relapse.
Journal ArticleDOI
A history of the study of solid tumour growth: the contribution of mathematical modelling.
Robyn P. Araujo,Donald McElwain +1 more
TL;DR: This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time, showing the crucial relationship between experimental and theoretical approaches.