Brief description
The project Convergence and Stability of Reaction and Interaction Network Dynamics (ConStRAINeD) deals with specific Continuous-Time Markov Chain models of interacting individuals called Stochastic Reaction Networks. The state space is the number of available individuals of different kinds, and transitions are encoded by a finite set of allowed reactions, which can be arranged as the edges of a reaction graph.
Example of a small reaction graph, composed by two reversible reactions.
Stochastic Reaction Networks are often used as models in biochemistry, epidemiology, and ecology. The aim of ConStRAINeD is to provide new theoretical insights on such models, in view of their concrete applications. ConStRAINeD has two main objectives, listed below.
Limit behavior
Developing theorems connecting the structure of the reaction graph with the existence of a long-term limit of the model, as well as with its characterization.
Spatial heterogeneity
Extending the setting of Stochastic Reaction Networks to cases in which spatial positions of particles are taken into account by introducing a random graph of interaction and diffusion dynamics. The effect that this has on the large volume dynamics will be studied.
The objectives mainly involve theorems based on the structure of the reaction or the interaction graph and therefore independent on
the specific rate parameters. This choice is motivated by the fact that the exact rates of changes in biological, epidemiological or
ecological systems are rarely known with precision. Hence, results that hold for a large class of parameters are both impactful and
mathematically challenging.