From Physics to Living Systems- Applicable Mathematical Models

Abstract

In the last three decades different mathematical methods and models have been developed for the modeling of living systems. Ordinary Differential Equations (ODE), Partial Differential Equations (PDE), kinetic theory approach, continuum mechanics approach, equilibrium and non equilibrium statistical mechanics are, among others, the most used frameworks. ODE-based models are employed for studying the time evolution of the density of the populations under consideration; PDE-based models deals with the evolution of systems with an internal structure (usually the age); kinetic theory models are concerned with the modeling of interactions among the entities; continuum mechanics approach is based on the fluid-assumption of the systems. Each framework is suitable for the modeling of the complex systems depending on what is needed to model. Recently investigation on a new mathematical framework which couples kinetic theory models with non equilibrium statistical mechanics tools (Gaussian thermostat), the so-called thermos tatted kinetic theory, has been summarized in [3]. This new framework requires a much more spread ground of research that must be, at the same time, accurate and rigorous, and is proposed for the modeling of physics systems and living systems.