Abstract
This article discusses some paradoxical results that arise when modelling uncertainties in models of anti-tumor chemotherapies using Gaussian noise. The effects of intrinsic and environmental perturbations and uncertainties on the dynamics of tumor growth and anti-tumor chemotherapy delivered via continuous infusion are considered.
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References
M. Peckham, H. M. Pinedo and U. Veronesi (Editors), Oxford Textbook of Oncology, 2nd edition, Oxford University Press, 2001.
C. A. Braumann, Harvesting in a Random Environment: Ito or Stratonovich calculus?, J. of Theoretical Biology 244 (2007), 424–432.
L. Zadeh, Fuzzy Sets, Information and Control 8 (1965), 338–353.
V. Krivan and G. Colombo, A Non-stochastic Approach for Modeling Uncertainty in Population Dynamics, Bulletin of Mathematical Biology 60 (1998), 721–751.
K. K. Majumdar and D. D. Majumder, Fuzzy Differential Inclusions in Atmospheric and Medical Cybernetics, IEEE Transactions on Systems, Man and Cybernetics 34 (2004), 877–887.
A. d’Onofrio, Fuzzy Oncology, Applied Mathematics Letters (in press, electronic version available at the webpage http://dx.doi.Org/10.1016/j.aml.2007.05.019).
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© 2008 Birkhäuser Verlag Basel/Switzerland
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d’Onofrio, A. (2008). “Noisy Oncology”: Some Caveats in using Gaussian Noise in Mathematical Models of Chemotherapy. In: Hosking, R.J., Venturino, E. (eds) Aspects of Mathematical Modelling. Mathematics and Biosciences in Interaction. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8591-0_12
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DOI: https://doi.org/10.1007/978-3-7643-8591-0_12
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8590-3
Online ISBN: 978-3-7643-8591-0
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