Explicit formulas for a continuous stochastic maturation model. Application to anticancer drug pharmacokinetics/pharmacodynamics.

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

1 UPTE - Physiopathologie et Toxicologie Expérimentales
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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. This approach allows the discussion of identifiability issues which are of difficult access for finite compartmental models. The article ends up with an example of application for anticancer drug pharmacokinetics/pharmacodynamics.

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

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

Djalil Chafai, Didier Concordet. Explicit formulas for a continuous stochastic maturation model. Application to anticancer drug pharmacokinetics/pharmacodynamics.. Stochastic Models, 2008, 24 (3), pp.376-400. ⟨10.1080/15326340802232244⟩. ⟨hal-00003498v3⟩