A mathematical model and numerical simulation for SARS‑CoV‑2 dynamics

Since its outbreak the corona virus-19 disease has been particularly aggressive for the lower respiratory tract, and lungs in particular. The dynamics of the abnormal immune response leading to lung damage with fatal outcomes is not yet fully understood. We present a mathematical model describing the dynamics of corona virus disease-19 starting from virus seeding inside the human respiratory tract, taking into account its interaction with the components of the innate immune system as classically and alternatively activated macrophages, interleukin-6 and -10. The numerical simulations have been performed for two different parameter values related to the pro-inflammatory interleukin, searching for a correlation among components dynamics during the early stage of infection, in particular pro- and anti-inflammatory polarizations of the immune response. We found that in the initial stage of infection the immune machinery is unable to stop or weaken the virus progression. Also an abnormal anti-inflammatory interleukin response is predicted, induced by the disease progression and clinically associated to tissue damages. The numerical results well reproduce experimental results found in literature.