Mathematical Biology

 

 

 

Objectives of the course : The course aims to train biology students in the quantitative analysis of biological systems. Students will be trained in how to use the language of mathematics to describe biological processes, how to write simple mathematical equations for various phenomena occurring in biology. Upon successful completion of the course the student(s) should have an understanding of:

- basic elements of mathematical modelling of biological systems and processes

- basic mathematical and computational modelling tools

- basic models from the areas of population biology, ecology, and epidemiology

and be able to

- understand the key questions in the field of modelling of biological processes

- study the behaviour of continuous and discrete in time dynamical systems

- use mathematical methods to study models qualitatively

- construct/review/extend a model based on experimental observations

 

Course contents:  

- Introduction to modelling of biological processes and systems.

- Modelling of physiological processes at the individual level. Introduction to  

  Dynamic Energy Budget (DEB) theory

- One-species population models (exponential and logistic models, Leslie matrix

  models)

- Two species population models: Predator-Prey, Competition,

   Mutualism/Symbiosis.

- Epidemiological Models e.g., SIR

- Enzyme reaction models

- Basic mathematical concepts: Dimensional analysis, Differential equations,

  Differential equations and systems of differential equations (qualitative

  analysis), Elements of linear algebra (matrices, eigenvalues and eigenvectors)