COVID-19 ORDER PARAMETERS AND ORDER PARAMETER TIME CONSTANTS OF ITALY AND CHINA: A MODELING APPROACH BASED ON SYNERGETICS
T.D. Frank
Abstract
From a dynamical systems perspective, COVID-19 infectious disease emerges via an instability in human populations. Accordingly, the human population free of COVID-19 infected individuals is an unstable state and the dynamics away from that unstable state is a bifurcation. Recent research has determined COVID-19 relevant bifurcation parameters for various countries in terms of basic reproduction ratios. However, little is known about the relevant order parameters (synergetics) of COVID-19 bifurcations and the corresponding time constants. Those order parameters describe directions in compartment model spaces in which infection dynamics initially evolves. The corresponding time constants describe the speed of the dynamics along those directions. COVID-19 order parameters and their time constants are derived within a standard SEIR dynamical systems framework and determined explicitly for two published studies on COVID-19 trajectories in Italy and China. The results suggest the existence of certain relationships between order parameters, time constants, and reproduction ratios. However, the examples from Italy and China also suggest that COVID-19 order parameters and time constants in general depend on regional differences and the stage of the local COVID-19 epidemic under consideration. These findings may help to improve the forecasting of COVID-19 outbreaks in new hotspots around the world.