Differential equations frameworks and models for the physics of biological systems

Abstract

The modeling of biological systems has recently gained much attention considering the possibility to describe the time evolution of a biological system by employing differential equations. Different frameworks have been proposed depending on the number of dynamic variables. Ordinary differential equations (ODE) are employed if time is the only dynamic variable; partial differential equations (PDE) are proposed when, in addition to the time variable, space and/or velocity variables are considered. In the context of differential equation models, new frameworks have been proposed where stochastic terms are added to classical deterministic terms. A specific model is proposed when the differential equations are coupled to initial and/or boundary conditions. This editorial article deals with the topic of this special issue, which is devoted to the new developments in the multiscale modeling of complex biological systems with special attention to the interplay between different scholars.