The Becker-Döring equation is among the wide class of coagulation-fragmentation equations and is one of the earliest descriptions of particle growth in the theory of nucleation from supersaturated vapour. This model describes the growth and decay of clusters, consisting of identical monomers, only by the addition and removal of monomers.

In this talk, motivated by enzymatic reactions in biology, we will introduce and analyse a variant of the Becker-Döring equations; this model incorporates irreversible fragmentation and monomer injection. After some recollection of coagulation-fragmentation equations, we will first present theoretical results on our model; we will establish global existence and uniqueness under some suitable conditions, and then we will focus on the long-time behaviour of our solution. Finally, we will present an efficient scheme that preserves the asymptotic and allows fast computation by sub-sampling the clusters.