Covid-19 Order Parameters and Order Parameter Time Constants of Italy and China: A Modeling Approach Based on Synergetics

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.

Rise and Decay of the COVID-19 Epidemics in the USA and the State of New York in the First Half of 2020: A Nonlinear Physics Perspective Yielding Novel Insights

“…Among the many ways to describe the time course of COVID-19 cases (e.g., by means of autoregressive integrated moving average models [15]), epidemiological compartment models such as susceptible-exposed-infected-recovered (SEIR) models [16,17] have been important tools to understand COVID-19 data and to examine the impact of intervention measures. Such SEIR models and generalized SEIR models have been used to examine COVID-19 epidemics in various countries around the globe [18][19][20][21][22][23]. For the current work, the study by Ngonghala et al [24] is of particular interest.…”

COVID-19: Analytic results for a modified SEIR model and comparison of different intervention strategies

“…At a sufficiently large time (but still in the very early phase of the pandemic) we equate the observed confirmed number on some day to which therefore gives us the relation This then tells us that we should start with the following initial conditions, (now counting time from the day of the observation ): The crucial point is that the leading eigenvector fixes the direction of the growth and then knowledge of linear combination fixes all the other coordinates . Thus, independent of initial conditions, the vector describing all the system variables quickly points along the direction of the eigenvector corresponding to the largest eigenvalue [15] , [28] . Hence if we know any one variable (or a linear combination of all the variables) at sufficiently large times in the growing phase, then the full vector is completely specified.…”

“…Several earlier work have discussed, using determinsitic compartmentalized models, the effect of asymptomatic affected population and the effect of intervention measures on the COVID pandemic [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] . Here we present a somewhat different choice of compartments and perform a careful quantitative comparison of different intervention strategies.…”

“…It is also not clear as to what is the ideal intervention strategy that a government should implement, while also taking into account the economic and social factors. The role of mathematical models has been to provide guidance for policy makers [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] .…”

Covid-19 Pandemic: Directed or Natural Fluctuation That Changes the World

“…N. Harari, a discussion of the famous modern European philosophers Giorgio Agamben (Agamben, 2020) and Jean-Luc Nancy regarding the Covid-19 pandemic and its impact on the formation of a new reality. We also relied on biology studies to model a modern pandemic based on a synergistic approach (Frank, 2020).…”