This paper focuses on the multiscale modeling of the COVID-19 pandemic and presents further developments of the model [7] with the aim of showing how relaxations of the confinement rules can generate sequential waves. Subsequently, the dynamics of mutations into new variants can be modeled. Simulations are developed also to support the decision making of crisis managers.

This paper deals with the modeling and simulation of the in-host dynamics of a virus. The modeling approach was developed according to the idea that mathematical models should go beyond deterministic single-scale population dynamics by taking into account the multiscale, heterogeneous features of the complex system under consideration. Here, we considered modeling the competition between the virus, the epithelial cells it infects, and the heterogeneous immune system with evolving activation states that induce a range of different effects on virus particles and infected cells. The subsequent numerical simulations showed different types of model outcomes: from virus elimination, to virus persistence and periodic relapse, to virus uncontrolled growth that triggers a blow-up in the fully activated immune response. The simulations also showed the existence of a threshold in the immune response that separates the regimes of higher re-infections from lower re-infections (compared to the magnitude of the first viral infection).