Theoretical Biology

Systems Medicine

of Infectious Diseases

Research Group

Mathematical Biology

 

Objectives: This course provides the student with the fundamental skills for a research career in the growing field of mathematical medicine and biology. Advanced nonlinear systems techniques will be covered to analyse mathematical models of infectious diseases e.g. HIV, ebola and influenza. In terms of specific maths topics, students do not need a deep mathematical background, but enthusiasm and a willingness to learn about it. Biological terminology will be introduced as necessary throughout the course. Modules are mainly delivered through lectures and problem classes for smaller groups.

 

Program

Module 1. Principles of Mathematical Modelling

  • Philosophy
  • Modelling approaches
  • Mass conservation and chemical reactions
  • Lotka Volterra and Epidemic Models
  • Study Case: HIV infection

 

Module 2. Linear Systems

  • Fundamentals of linear algebra
  • System significance of eigenvectors and eigenvalues
  • Stability, controlability and observability

 

Module 3. Nonlinear Systems

  • Nonlinear phenomena
  • Equilibrium points and Linearization
  • Qualitative behaviour near the equilibrium
  • Bifurcation Analysis
  • Lyapunov Stability
  • Study case: Ebola vius infection

 

Module 4. Identification Systems

  • Inverse Problem
  • Some optimization concepts
  • Parameter Estimation
  • Structural and Practical Identifiability
  • Bootstrap and Monte Carlo Simulations
  • Study case: Influenza virus infection

 

 

Previous Courses: Technische Universität Braunschweig (Summer 2012, Winter 2015)

 

 

 

 

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