Mathematical model and numerical simulation for interleukins-driven macrophage promotion and TNF - alpha influence on SARS-CoV-2 dynamics

A fatal event which can happen in patients affected by the SARS-CoV-2 disease is the cytokine storm, a mechanism leading to the production of several types of cytokines causing lethal lung damages. The mutual interactions among pro- and anti-inflammatory immune agents and SARS-CoV-2 virions occurring during the disease development are modelled in the frame of the mass conservation leading to a system of reaction-diffusion-taxis partial differential equations. In particular, the interaction of SARS-CoV-2 with a system of cytokines, macrophages, and T lymphocytes, is modelled implementing some parameters suitable to investigate the macrophage contribution to the system dynamics through interleukins deactivation. The numerical results indicate that interleukins deactivation slightly affects the virus dynamics which remains in the context of a rapidly worsening disease. A pro-inflammatory behaviour of interleukin-10 consistent with a pleiotropic role is predicted, as reported in clinical findings. The contribution of tumour necrosis factor-α to the overall dynamics results in an increase of the proinflammatory response and, unexpectedly, also the virus production. Some cues suggest possible pathways for therapeutic strategies against the COVID-19 disease.