MA 493/BIO 495 (Spring): Mathematical Modeling Techniques for Biological Systems

Course Topics

  1. Modeling Philosophy (2 days)
  2. Forward Problems vs. Inverse Problems (1 day)
  3. Motivating Examples (1 week)
    • Population Dynamics
    • Physiologically-Based Pharmacokinetic (PBPK) Models
  4. MATLAB (1 week)
  5. Numerical Methods of Ordinary Differential Equations (3 weeks)
    • One-step methods
    • Adaptive step length
    • Case study: PBPK Models
  6. Numerical Optimization (2 weeks)
    • Gradient-based methods
    • Sampling-based methods
    • Case study: Heat Diffusion Process in a Rod: Parameter Estimation
  7. Sensitivity Analysis (2 weeks)
    • Local and global sensitivities
    • Finite-difference approximation
    • Automatic differentiation
  8. Case study: Population Dynamics
  9. Identifiability Analysis and Subset Selection (2 weeks)
    • Case study: HIV Dynamic Model
  10. Statistical Aspects of Inverse Problems (3 weeks)
    • Case study: PBPK Models

Remarks: All topics will be discussed in the context of specific modeling projects that are being studied in government research labs and private companies. In fact, in some cases students will be exposed to specific laboratory experiments, data collection and analysis.

Undergraduate Biomathematics at NC State

This course is part of a new undergraduate biomathematics (UBM) initiative at NC State. Funded by the National Science Foundation, the UBM program offers you the chance to carry out cutting-edge research at the interface of mathematics and biology. Eight students a year, four from the mathematical sciences and four from the biological sciences, will receive summer support as part of a year-long research experience. MA 493 (Fall semester) and its sister course MA 493 (Spring semester) are designed to prepare biology students for the research component of the UBM program.