Grant Details

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 (SRNs). 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. SRNs are often used as models in biochemistry, epidemiology, and ecology. The aim of ConStRAINeD is to provide new theoretical insights on SRNs which are crucial to unlock a deeper understanding in important applications. ConStRAINeD has two main objectives, listed below. Objective 1: developing theorems connecting the structure of the reaction graph with the positive recurrence of the model, as well as with an exact description of the stationary distributions. Objective 2: extending the setting of SRN 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 interesting.