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Mathematical Model of BCG Immunotherapy in Superficial Bladder Cancer

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Abstract

Immunotherapy with Bacillus Calmette–Guérin (BCG)—an attenuated strain of Mycobacterium bovis (M. bovis) used for anti tuberculosis immunization—is a clinically established procedure for the treatment of superficial bladder cancer. However, the mode of action has not yet been fully elucidated, despite much extensive biological experience. The purpose of this paper is to develop a first mathematical model that describes tumor-immune interactions in the bladder as a result of BCG therapy. A mathematical analysis of the ODE model identifies multiple equilibrium points, their stability properties, and bifurcation points. Intriguing regimes of bistability are identified in which treatment has potential to result in a tumor-free equilibrium or a full-blown tumor depending only on initial conditions. Attention is given to estimating parameters and validating the model using published data taken from in vitro, mouse and human studies. The model makes clear that intensity of immunotherapy must be kept in limited bounds. While small treatment levels may fail to clear the tumor, a treatment that is too large can lead to an over-stimulated immune system having dangerous side effects for the patient.

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Authors and Affiliations

  1. Biomathematics Unit, Department of Zoology, Faculty of Life Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Svetlana Bunimovich-Mendrazitsky & Lewi Stone

  2. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    Eliezer Shochat

Authors
  1. Svetlana Bunimovich-Mendrazitsky
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  2. Eliezer Shochat
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  3. Lewi Stone
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Correspondence to Lewi Stone.

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Bunimovich-Mendrazitsky, S., Shochat, E. & Stone, L. Mathematical Model of BCG Immunotherapy in Superficial Bladder Cancer. Bull. Math. Biol. 69, 1847–1870 (2007). https://doi.org/10.1007/s11538-007-9195-z

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  • DOI: https://doi.org/10.1007/s11538-007-9195-z

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