Mathematical modeling has become an integral part of different fields of biology, from ecology to cell biology. This course will introduce students of biology to elementary mathematical concepts and tools for dynamical models. The course will focus on modeling using ordinary differential equations (ODEs). We will start with basic mathematical concepts of ODE-based models and then connect those with experimental biology. Mathematical models will be on cellular and molecular processes in biology, like cell signaling, and transcriptional networks. Students will learn basics of analytical techniques, graphical techniques, and numerical simulation.INTENDED AUDIENCE: Students of Biotechnology, Biology, Mathematical Biology, and allied subjects.PREREQUISITES: Must have studied Mathematics at 10+2 level. Have studied graduate-level Biochemistry and Molecular Biology. Knowledge of Computer Programming will be helpful but not a necessity.INDUSTRY SUPPORT: Bio-pharma industries use cellular level as well organism level mathematical models. This course would help to initiate biologists to such modeling.
Week 1 :
L1: Introduction to mathematical modeling in biology
L2: How to start modeling?
L3: Basic concepts of modeling using ODEs: Modeling the spread of infectious disease
L4: Basic concepts of modeling using ODEs: Modeling population growth
L5: Numerical solution of ODE-based models - I
L6: Numerical solution of ODE-based models - II
Week 2 :
L1: Simulating ODE-based models: Introduction to JSim
L2: Simulating ODE-based models: Examples of simulation in JSim
L3: Steady state and stability analysis: Understanding steady state
L4: Steady state and stability analysis: Stability of steady states