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We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…

In living cells, biochemical reactions are catalyzed by specific enzymes and connect to one another by sharing substrates and products, forming complex networks. In our previous studies, we established a framework determining the responses…

In this paper we study a class of stochastic chemical reaction networks (CRNs) for which chemical species are created by a sequence of chain reactions. We prove that under some convenient conditions on the initial state, some of these…

The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence…

We introduce a mixed-integer linear programming (MILP) framework capable of determining whether a chemical reaction network possesses the property of being endotactic or strongly endotactic. The network property of being strongly endotactic…

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…

We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…

Continuous time Markov chains are commonly used as models for the stochastic behavior of chemical reaction networks. More precisely, these Stochastic Chemical Reaction Networks (SCRNs) are frequently used to gain a mechanistic understanding…

Stochastic reaction networks with mass-action kinetics provide a useful framework for understanding processes -- biochemical and otherwise -- in homogeneous environments. However, cellular reactions are often compartmentalized, either at…

Stochastic models of reaction networks are becoming increasingly important in Systems Biology. In these models, the dynamics is generally represented by a continuous-time Markov chain whose states denote the copy-numbers of the constituent…

Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning…

Many biological systems can be modeled as a chemical reaction network with unknown parameters. Data available to identify these parameters are often in the form of a stationary distribution, such as that obtained from measurements of a cell…

We consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…

The dynamics of a chemical reaction network (CRN) is often modelled under the assumption of mass action kinetics by a system of ordinary differential equations (ODEs) with polynomial right-hand sides that describe the time evolution of…

In this paper we develop the elements of the theory of algorithmic randomness in continuous-time Markov chains (CTMCs). Our main contribution is a rigorous, useful notion of what it means for an individual trajectory of a CTMC to be random.…

Markov chains on the non-negative quadrant of dimension $d$ are often used to model the stochastic dynamics of the number of $d$ entities, such as $d$ chemical species in stochastic reaction networks. The infinite state space poses…

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large…

Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology,…

The quantitative convergence to equilibrium for reaction-diffusion systems arising from complex balanced chemical reaction networks with mass action kinetics is studied by using the so-called entropy method. In the first part of the paper,…

Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good…