Papers by Sandip Banerjee
Mathematical biosciences, Jan 1, 2005
The paper aims to express the spontaneous regression and progression of a malignant tumor system ... more The paper aims to express the spontaneous regression and progression of a malignant tumor system as a prey–predator like system. The model is a three dimensional deterministic system, consisting of tumor cells, hunting predator cells and resting predator cells. Local ...
Applied Mathematics and Computation, Jan 1, 2006
Applied Mathematics …, Jan 1, 2007
Journal of Applied …, Jan 1, 2002
International Journal of …, Jan 1, 2000
National Conference on Nonlinear …, Jan 1, 2006
Journal of Biological …, Jan 1, 2008
This paper deals with the interaction between dispersed cancer cells and the major populations of... more This paper deals with the interaction between dispersed cancer cells and the major populations of the immune system, namely, the T helper cells, T Cytotoxic cells, B cells, and antibodies produced. The system is described by a set of five ordinary differential equations. Both ...
Anaesthesia &intensive care medicine, Jan 1, 2005
Systems Analysis Modelling …, Jan 1, 1997
... Collaborative Colleagues: Sandip Banerjee: colleagues. CG Chakrabarti: colleagues. The ACM Po... more ... Collaborative Colleagues: Sandip Banerjee: colleagues. CG Chakrabarti: colleagues. The ACM Portal is published by the Association for Computing Machinery. Copyright © 2009 ACM, Inc. Terms of Usage Privacy Policy Code ...
International Journal of Applied Mathematics and …, Jan 1, 2008
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, ... more The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
Journal of Biological Physics, Jan 1, 1999
The paper first deals with the linear stability analysis of an activator-inhibitor reaction diffu... more The paper first deals with the linear stability analysis of an activator-inhibitor reaction diffusion system to determine the nature of the bifurcation point of the system. The non-linear bifurcation analysis determining the steady state solution beyond the critical point enables us to determine characteristic features of the spatial inhomogeneous pattern formation arising out of the bifurcation of the state of the system.
Arxiv preprint arXiv:1105.3669, Jan 1, 2011
A mathematical modeling of Hepatitis C Virus (HCV) dynamics has been presented in this paper. The... more A mathematical modeling of Hepatitis C Virus (HCV) dynamics has been presented in this paper. The proposed model, which involves four coupled ordinary differential equations, describes the interaction of target cells (hepatocytes), infected cells, infectious virions and non-infectious virions. The model takes into consideration the addition of ribavirin to interferon therapy and explains the dynamics regarding biphasic and triphasic decline of viral load in the model. A critical drug efficiency parameter has been defined and it is shown that for efficiencies above this critical value, HCV is eradicated whereas for efficiencies lower this critical value, a new steady state for infectious virions is reached, which is lower than the previous steady state.
Journal of Biological …, Jan 1, 2010
Journal of Biological Systems, Vol. 18, No. 1 (2010) 7591 c World Scientific Publishing Company ... more Journal of Biological Systems, Vol. 18, No. 1 (2010) 7591 c World Scientific Publishing Company DOI: 10.1142/S0218339010003226 ... A CONTROL THEORY APPROACH TO CANCER REMISSION AIDED BY AN OPTIMAL THERAPY ... SIDDHARTHA P. CHAKRABARTY Department of ...
Arxiv preprint arXiv:1006.5069, Jan 1, 2010
A mathematical model for the quantitative analysis of cancer immune interaction, considering the ... more A mathematical model for the quantitative analysis of cancer immune interaction, considering the role of antibodies has been proposed in this paper. The model is based on the clinical evidence, which states that antibodies can directly kill cancerous cells . The existence of transcritical and saddle-node bifurcation, which has been proved using Sotomayor theorem, provides strong biological implications. Through numerical simulations, it has been illustrated that under certain therapy (like monoclonal antibody therapy), which is capable of altering the parameters of the system, cancer-free state can be obtained.
Mathematical biology, Jan 1, 2006
Uploads
Papers by Sandip Banerjee