Modeling and Control in the Biomedical Sciences

1. Front Matter

   Pages N1-V

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2. A Brief Review of Enzyme Kinetics

   • H. T. Banks

   Pages 1-12

3. Models for Enzymatically Active Membranes

   • H. T. Banks

   Pages 13-26

4. Modeling of Enzyme Cascades

   • H. T. Banks

   Pages 27-51

5. Modeling and Control of Epidemics

   • H. T. Banks

   Pages 52-66

6. Modeling of the Control System in Glucose Homeostasis

   • H. T. Banks

   Pages 67-75

7. Modeling and Control of Tumor Growth

   • H. T. Banks

   Pages 76-89

8. A Survey of Recent Efforts

   • H. T. Banks

   Pages 90-103

9. Back Matter

   Pages 104-114

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These notes are based on (i) a series of lectures that I gave at the 14th Biennial Seminar of the Canadian Mathematical Congress held at the University of Western Ontario August 12-24, 1973 and (li) some of my lectures in a modeling course that I have cotaught in the Division of Bio-Medical Sciences at Brown during the past several years. An earlier version of these notes appeared in the Center for Dynamical Systems Lectures Notes series (CDS LN 73-1, November 1973). I have in this revised and extended version of those earlier notes incorporated a number of changes based both on classroom experience and on my research efforts with several colleagues during the intervening period. The narrow viewpoint of the present notes (use of optimization and control theory in biomedical problems) reflects more the scope of the CMC lectures given in August, 1973 than the scope of my own interests. Indeed, my real interests have included the modeling process itself as well as the contributions made by investiga­ tors who employ the techniques and ideas of control theory, systems analysis, dif­ ferential equations, and stochastic processes. Some of these contributions have quite naturally involved application of optimal control theory. But in my opinion many of the interesting efforts being made in modeling in the biomedical sciences encompass much more than the use of control theory.

• Biologisches Modell
• Biomathematik
• Control
• Derivation
• Modeling

• Lefschetz Center for Dynamical Systems Division of Applied Mathematics, Brown University, Providence, USA

  H. T. Banks

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