Hybrid Modelling in Biology: a Classification Review

A Stéphanou (1) , Vitaly Volpert (2, 3)

1 TIMC-IMAG-DyCTiM2 - Dynamiques Cellulaire et Tissulaire - Interdisciplinarité, Modélisation & Microscopie
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
3 MMCS - Modélisation mathématique, calcul scientifique

This paper presents a general review on hybrid modelling which is about to become ubiquitous in biological and medical modelling. Hybrid modelling is classically defined as the coupling of a continuous approach with a discrete one, in order to model a complex phenomenon that cannot be described in a standard homogeneous way mainly due to its inherent multiscale nature. In fact, hybrid modelling can be more than that since any types of coupled formalisms qualify as being hybrid. This review first presents the evolution and current context of this modelling approach. It then proposes a classification of the models through three different types that relate to the nature and level of coupling of the formalisms used.

Mots clés: 92C42; 68R0; system biology; multiscale; hybrid model; 92B05; Mathematics Subject Classification: 35Q92; and phrases: complex system; discrete–continuous; 92C50; 93A30; 93C55

Domaines: Equations aux dérivées partielles [math.AP]

A Stéphanou, Vitaly Volpert. Hybrid Modelling in Biology: a Classification Review. Mathematical Modelling of Natural Phenomena, 2016, 11, pp.37 - 48. ⟨10.1051/mmnp/201611103⟩. ⟨hal-01397430⟩