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

Abstract

The relevant dynamics underlying COVID-19 waves is described from an amplitude space perspective. To this end, the amplitude dynamics of infected populations is considered in different stages of epidemic waves. Eigenvectors and their corresponding amplitudes are derived analytically for low-dimensional models and by means of computational methods for high-dimensional models. It is shown that the amplitudes of all eigenvectors as functions of time can be tracked through the diverse stages of COVID-19 waves featuring jumps at the stage boundaries. In particular, it is shown that under certain circumstances the initial, outbreak stage and the final, subsiding stage of an epidemic wave are primarily determined by the unstable eigenvector of the initial stage and its corresponding remnant vector of the final stage. The corresponding amplitude captures most of the dynamics of the emerging and subsiding epidemics such that the problem at hand effectively becomes one dimensional leading to a dramatic reduction of the complexity of the problem at hand. Explicitly demonstrated for the first-wave COVID-19 epidemics of the year 2020 in the state of New York and Pakistan are given.

COVID-19: respiratory disease diagnosis with regularized deep convolutional neural network using human respiratory sounds

“…Natiq and Saha implemented a non-linear dynamical model by combining of susceptible infected and recovered (SIR) model and Lotka-Volterra model to identify the virus transmission between the various species [58]. The researchers are also focused on mathematical models, non-linear dynamic models, and prediction models to determine the seriousness of the virus, how the vaccination is distributed to the people, how vaccination gives immunity to the human body, and the death rate in various countries [59][60][61][62][63].…”

“…: V,-vol 2/COVID-19 is spreading between different species. The researchers are also focused on mathematical models, non-linear dynamic models, and prediction models to identify the seriousness of the virus, how the vaccination is distributed to the people, how vaccination gives immunity to our body, and the death rate in various countries [59][60][61][62][63].…”

Unstable eigenvectors and reduced amplitude spaces specifying limit cycles of coupled oscillators with simultaneously diagonalizable matrices: with applications from electric circuits to gene regulation

“…(99) were then computed from the diagonal matrices D A and D B (whose coefficients are listed above) by inverting the steps shown in Eq. (19). That is, A = MD A M −1 and B = MD B M −1 .…”

“…( 99) was taken as the second row vector of M −1 as discussed above (or see again Refs. [18,19]). Figures 5 and 6 present the simulation results.…”

“…This fundamental framework for the description of systems close to instabilities has been introduced several decades ago [1,[5][6][7][8]. Since then, it has produced a steady stream of new applications in contemporary research [9][10][11][12][13][14][15][16][17] (see in particular recent applications in COVID-19 research [18][19][20]), which illustrates the important task to make the eigenvector/eigenfunction framework available in research fields that have not yet taken fully advantage of this approach. On the other hand, coupled oscillator systems have been comprehensively studied [21,22], in particular, to identify their characteristic a e-mail: till.frank@uconn.edu (corresponding author) attractors.…”