Simplicity From Complexity: On the Simple Amplitude Dynamics Underlying Covid-19 Outbreaks in China

Abstract

COVID-19 confronts societies and individuals with unprecedented challenges. It is advocated that complex systems theory, in general, and synergetics, in particular, provide a valuable and comprehensive repertoire of tools and concepts such as the concept of amplitude equations and order parameters to study the spread of COVID-19 in human populations. Specifically, within the framework of SIR and SEIR compartment models COVID-19 trajectories are described in terms of amplitude equations and order parameters. By plotting simulated and semi-empirical COVID-19 case trajectories it is shown that the initial epidemics in China, in general, and Wuhan city, in particular, during the first quarter of the year 2020 followed relatively simple amplitude dynamics in SIR and SEIR model state spaces describing interaction classes of individuals. The amplitudes evolve along certain paths or directions determined by order parameters that are well known to exist in complex systems. In summary, the present work highlights that COVID-19 outbreaks are constrained by general principles that hold for a broad class of phenomena in living and non-living systems.

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

“…The benefits of this approach has been demonstrated in previous works. Pervious works on the epidemiological level have suggested that COVID-19 outbreaks in populations evolve along unstable eigenvectors [8,[49][50][51][52][53]. Figure 1 (panels (a) and (b)) shows results that illustrate this point and have been obtained in earlier studies by Pang et al [7] and Frank [8,50].…”

Characterizing stages of COVID-19 epidemics: a nonlinear physics perspective based on amplitude equations

“…The eigenvectors of read The perturbation involves . The amplitude equations can be found in previous studies [ 12 , 13 , 15 ] and read with where | M | denotes the determinant of the eigenvector matrix: and . The dynamics of the non-infected system is given by Furthermore, the mappings and read explicitly and The amplitude space description of the SEIR model will be used below to show how to describe stages of COVID-19 epidemics in amplitude space.…”

“…The perturbation u = X − X st = (E, I, u 3 , R) involves u 3 = S − N ≤ 0. The amplitude equations can be found in previous studies [12,13,15] and read…”

“…In previous studies it has been pointed out that the relevant unstable eigenvector [9] or order parameter [7,11] determines the initial stage of a COVID-19 wave [12][13][14]. In particular, it has been demonstrated that a e-mail: till.frank@uconn.edu (corresponding author) the dynamics of an epidemic converges towards the dominant sub-dynamics along the unstable eigenvector [15] and it has been recognized that the amplitude equation perspective based on eigenvalues and eigenvectors naturally leads to a three-stage scheme of COVID-19 waves [16][17][18][19].…”

Spreading of Infections on Network Models: Percolation Clusters and Random Trees

“…It has been studied extensively also in the realm of statistical physics of disordered systems (e.g., [17][18][19]). More recently, a great deal of interest has been devoted to the study and development of new scenarios to describe COVID-19 spreading [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In addition, we can mention that a lot of attention has been drawn to population structures displaying complex and heterogeneous connectivity patterns, as well as to the associated dynamics of epidemic and infection spreading processes in the so-called metapopulation models [36,37].…”