Amplitude Equations And Order Parameters Of Human Sars-Cov-2 Infections And Immune Reactions: A Model-Based Approach

Several recent modeling studies have attempted to understand the human immune reaction to SARS-CoV-2 infections. Such a model-based understanding provides a sound basis for fighting COVID-19 on the level of individual patients. However, in this context, a worked-out nonlinear physics analysis providing insights into underlying amplitude equations and potential COVID-19 order parameters has not been conducted so far. In order to conduct such an analysis, a three-variable virus dynamics model is considered that can account for the human immune reaction to SARS-CoV-2 infections. The model amplitudes equations are derived and the relevant order parameter is determined. In line with theoretical reasoning, it is demonstrated that the order parameter and its amplitude determine the initial stage of SARS-CoV-2 infections, in general, and the initial dynamics of immune reactions, in particular. Explicitly, this finding is demonstrated for data from four COVID-19 patients. For those patients it is also demonstrated that the remnant of the order parameter determines the final disease decline phase. In this context, a time-resolved eigenvalue analysis is conducted that reveals that the transition from the initial stage to the decline stage which is associated with a switch of the leading eigenvalue from a positive to a negative value. It is argued that the immune reaction essentially contributes to this switch. From a medical-physics point of view, this observation suggests that the immune reaction of COVID-19 patients can stabilize the virus-free fixed point of affected sites.