Active particles methods towards modeling in science and society

TL;DR

This paper introduces a mathematical framework for modeling large systems of interacting living entities, aiming to describe their collective behaviors through differential models, with applications and future research directions.

Contribution

It develops a new mathematical method for modeling collective behaviors in living systems and demonstrates its application through case studies.

Findings

Derived a mathematical method for living systems modeling

Applied the method to various case studies

Outlined future research directions

Abstract

This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors by differential models. The contents is in three parts. Firstly, we derive the mathematical method; subsequently, we show how the method can be applied in a number of case studies related to well defined living systems and finally, we look ahead to research perspectives focusing both on mathematical methods and further applications.