What is the in-host dynamics of SARS-CoV-2 virus? A challenge within a multiscale vision of living systems

This paper deals with the modeling and simulation of the in-host dynamics of a virus. The modeling approach is 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 consider 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 show different types of model outcomes: from virus elimination, to virus persistance and periodic relapse, and virus uncontrolled growth that triggers a blow-up in the fully-activated immune response. The simulations also show 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).