SARS-coronavirus-2 infections: biological instabilities characterized by order parameters

A four-variable virus dynamics TIIV model was considered that involves infected cells in an eclipse phase. The state space description of the model was transferred into an amplitude space description which is the appropriate general, nonlinear physics framework to describe instabilities. In this context, the unstable eigenvector or order parameter of the model was determined. Subsequently, a model-based analysis of viral load data from eight symptomatic COVID-19 patients was conducted. For all patients, it was found that the initial SARS-CoV-2 infection evolved along the respective patient-specific order parameter, as expected by theoretical considerations. The order parameter amplitude that described the initial virus multiplication showed doubling times between 30 min and 3 h. Peak viral loads of patients were linearly related to the amplitudes of the patient order parameters. Finally, it was found that the patient order parameters determined qualitatively and quantitatively the relationships between the increases in virus-producing infected cells and infected cells in the eclipse phase. Overall, the study echoes the 40 years old suggestion by Mackey and Glass to consider diseases as instabilities.