The modelling and simulation of chemical reaction kinetics is of central relevance for many applications, e.g. in medicine or biochemistry. This lecture will provide an overview of the existing mathematical modelling approaches. Based on the theory of Markov processes, we will analyse the differences and connections between the models and consider several applications. We will discuss stochastic models based on Markov jump processes and stochastic differential equations, their limit behaviour for large particle numbers or fast reactions, as well as resulting deterministic-stochastic hybrid models. Numerical solution methods and simulation tools will be discussed and implemented in the exercises.
Open research questions can offer subjects for master theses or doctoral thesis.