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**SUMMER SCHOOL**

# CHEMICAL REACTION NETWORKS

Chemical Reaction Networks (CRNs) are popular mathematical models of several phenomena in system biology, epidemiology, population dynamics, telecommunications, chemistry. In such models, individuals are identical units (e.g. molecules), classified into several groups (e.g. chemical species) and interact through the so-called reactions. A reaction means, for example, an individual eating one of another group, or dying, or reproducing, as well as a protein binding with the RNA to regulate gene expression.

Reactions (as it happens in chemistry) are organised in a graph. CRNs can be modelled both as deterministic dynamical systems or stochastic systems (continuous time Markov chains). Deterministic dynamical systems describe the concentration of each reactant, and this modelling paradigm is suitable when the molecule number is very high. In both cases, it is often impossible to find solutions of the dynamical equations.

During the school, the following significant contributions to the theory of CRNs will be addressed: guessing some qualitative behaviour of the system (like the existence of stable equilibria, or of stationary or quasi-stationary distributions) from the properties of the reaction graph; approximating complicated systems with simpler ones (e.g. some with less reactants), or with different models that can be solved or simulated more easily.

Moreover, we will review some applications of CRNs to important real problems, including some statistical methodology that is required to fit the real data.