Numerical solution of the temporal dynamics of SARS-CoV-2 infection in patients with severe or critical clinical manifestations of COVID-19

Abstract

COVID-19 is an infectious disease caused by the SARS-CoV-2 coronavirus that started in Wuhan (China) in late 2019 and has spread across the world. When the patient enters the severe clinical features of the disease, the immune system begins to produce pro-inflammatory cytokines in an uncontrolled way, a phenomenon known as ``cytokine storm'', causing Acute Respiratory Distress Syndrome (ARDS) and, from there, the patient's clinical condition is critical, requiring hospitalization in Intensive Care Units (ICU). In this article, we developed a mathematical model that describes the problem of temporal dynamics of SARS-CoV-2 infection in patients with severe or critical clinical manifestations of COVID-19; as a consequence, the problem includes the ``cytokine storm''. The model consists of a system of five first-order nonlinear ordinary differential equations, which is numerically solved using the Mathematica Software. Among the five variables involved in the system, viral load was the most detailed, as it describes the level of SARS-CoV-2 RNA in patients. Viral load profiles were presented and interpreted, in several situations, in which patients progressed to cure or death. For viral load, the model showed a relative error of 19.13% when compared to clinical data from the existing literature