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Regulatory gene networks contain generic modules like those involvingfeedback loops, which are essential for the regulation of many biologicalfunctions. We consider a class of self-regulated genes which are the buildingblocks of many regulatory gene networks, and study the steady statedistributions of the associated Gillespie algorithm by providing efficientnumerical algorithms. We also study a regulatory gene network of interest insynthetic biology and in gene therapy, using mean-field models with timedelays. Convergence of the related time-nonhomogeneous Markov chain isestablished for a class of linear catalytic networks with feedback loops

Stochastic models and numerical algorithms for a class of regulatory gene networks