  This paper presents a critical analysis of the literature and perspective
research ideas for modeling the epidemics caused by the SARS-CoV-2 virus. It
goes beyond deterministic population dynamics to consider several key
complexity features of the system under consideration. In particular, the
multiscale features of the dynamics from contagion to the subsequent dynamics
of competition between the immune system and the proliferating virus. Other
topics addressed in this work include the propagation of epidemics in a
territory, taking into account local transportation networks, the heterogeneity
of the population, and the study of social and economic problems in populations
involved in the spread of epidemics. The overall content aims to show how new
mathematical tools can be developed to address the above topics and how
mathematical models and simulations can contribute to the decision making of
crisis managers.
