A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world.

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS-CoV-2 Severe Acute Respiratory Syndrome, corona virus n.2. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focussed also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.

On the interplay between mathematics and biology: hallmarks toward a new systems biology.

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach.

Complex multicellular systems and immune competition: new paradigms looking for a mathematical theory.

This chapter deals with the modeling and simulation of large systems of interacting entities whose microscopic state includes not only geometrical and mechanical variables (typically position and velocity), but also biological functions or specific activities. The main issue looks at the development of a biological mathematical theory for multicellular systems. The first part is devoted to the derivation of mathematical structures to be properly used to model a variety of biological phenomena with special focus on immune competition. Then, some specific applications are proposed referring to the competition between neoplastic and immune cells. Finally, the last part is devoted to research perspectives towards the objective of developing a mathematical-biological theory. A critique is presented of what has already been achieved towards the above target and what is still missing with special focus on multiscale systems.