# American Institute of Mathematical Sciences

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June  2013, 18(4): 1053-1076. doi: 10.3934/dcdsb.2013.18.1053

## B cell chronic lymphocytic leukemia - A model with immune response

 1 Tata Institute of Fundamental Research, Centre for Applicable Mathematics, Bangalore 560065, India 2 Department of Mathematics, Harvey Mudd College, Claremont, CA 91711 3 Department of Mathematics, Pomona College, Claremont, CA, 91711, United States

Received  August 2012 Revised  October 2012 Published  February 2013

B cell chronic lymphocytic leukemia (B-CLL) is known to have substantial clinical heterogeneity. There is no cure, but treatments allow for disease management. However, the wide range of clinical courses experienced by B-CLL patients makes prognosis and hence treatment a significant challenge. In an attempt to study disease progression across different patients via a unified yet flexible approach, we present a mathematical model of B-CLL with immune response, that can capture both rapid and slow disease progression. This model includes four different cell populations in the peripheral blood of humans: B-CLL cells, NK cells, cytotoxic T cells and helper T cells. We analyze existing data in the medical literature, determine ranges of values for parameters of the model, and compare our model outcomes to clinical patient data. The goal of this work is to provide a tool that may shed light on factors affecting the course of disease progression in patients. This modeling tool can serve as a foundation upon which future treatments can be based.
Citation: Seema Nanda, Lisette dePillis, Ami Radunskaya. B cell chronic lymphocytic leukemia - A model with immune response. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 1053-1076. doi: 10.3934/dcdsb.2013.18.1053
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