A continuous stochastic maturation model

Djalil Chafai (1, 2) , Didier Concordet (1, 2)

1 LSP - Laboratoire de Statistique et Probabilités
2 UPTE - Physiopathologie et Toxicologie Expérimentales

We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the system output under inhomogeneous killing and when the input follows a time-inhomogeneous Poisson process. Identifiability issues are discussed, and an application to the modelling of the toxicity of anti-cancer drugs is given. Such models can be seen in particular as generalisations of previous works of Jacquez & Simon and Schuhmacher & Thieme.

Mots clés: Compartmental systems; time lags; maturation models; stochastic modelling; Markov processes; inhomogeneous Markov processes; birth and death processes; queueing systems; point processes; Feynman-Kac formulae; jump processes.; jump processes

Domaines: Probabilités [math.PR]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Djalil Chafai, Didier Concordet. A continuous stochastic maturation model. 2004. ⟨hal-00003498v1⟩