My research interests concern stochastic mathematical models for biochemical reaction network. When few molecules of reactant species are present, the biological system is tipically modelled by means of continuous-time Markov chains.
In this setting, the study of possible connections between dynamical features and graphical properties of the model is of great interest. An obvious reason for this is that much more effort is usually needed to infer dynamical properties rather than graphical conditions. In the deterministic setting (that is, the changes of the reactant concentrations are modelled by ordinary differential equations) such connections have been studied for a long time, while in the stochastic setting this research area is still largely unexplored.
Possible simplifications of a model is another topic of interest. Indeed, biochemical systems are often analytically and computationally intractable, due to their high dimension and complexity. In particular, I am concerned about the elimination of chemical reactions and chemical species from the original model, or about transformations of them that can lead to a dimensional reduction of the problem, while still mantaining certain dynamical feature of interest.
Finally, I am interested in the relationship between stochastic and deterministic models under different points of view. In particular, I work on the limit behaviour of the systems, and on the relationship between limit behaviours of full and simplified networks and between stochastic and deterministic models.