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

Abstract

As of December 2020, since the beginning of the year 2020, the COVID-19 pandemic has claimed worldwide more than 1 million lives and has changed human life in unprecedented ways. Despite the fact that the pandemic is far from over, several countries managed at least temporarily to make their first-wave COVID-19 epidemics to subside to relatively low levels. Combining an epidemiological compartment model and a stability analysis as used in nonlinear physics and synergetics, it is shown how the first-wave epidemics in the state of New York and nationwide in the USA developed through three stages during the first half of the year 2020. These three stages are the outbreak stage, the linear stage, and the subsiding stage. Evidence is given that the COVID-19 outbreaks in these two regions were due to instabilities of the COVID-19 free states of the corresponding infection dynamical systems. It is shown that from stage 1 to stage 3, these instabilities were removed, presumably due to intervention measures, in the sense that the COVID-19 free states were stabilized in the months of May and June in both regions. In this context, stability parameters and key directions are identified that characterize the infection dynamics in the outbreak and subsiding stages. Importantly, it is shown that the directions in combination with the sign-switching of the stability parameters can explain the observed rise and decay of the epidemics in the state of New York and the USA. The nonlinear physics perspective provides a framework to obtain insights into the nature of the COVID-19 dynamics during outbreak and subsiding stages and allows to discuss possible impacts of intervention measures. For example, the directions can be used to determine how different populations (e.g., exposed versus symptomatic individuals) vary in size relative to each other during the course of an epidemic. Moreover, the timeline of the computationally obtained stages can be compared with the history of the implementation of intervention measures to discuss the effectivity of such measures.

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

“…Consistent with this approach and in line with previous three-stage epidemic models [ 16 , 18 ], in Ref. [ 19 ] a three-stage application of the model ( 30 ) was discussed in which was varied throughout three stages. The analysis focused on the five infected compartments .…”

“…In an initial study, a ten-variable generalized SEIR model was developed to examine the COVID-19 outbreak in the state of New York [ 39 ]. In a subsequent study, the model was used to examine the time course of the entire first-wave COVID-19 epidemic in the state of New York during the first half of 2020 [ 19 ]. Detailed descriptions of the model can be found in Refs.…”

“…Detailed descriptions of the model can be found in Refs. [ 19 , 39 ]. In what follows the model will be reviewed only briefly.…”

“…Finally, the model also addresses the compartment of recovered COVID-19 cases ( R ) and the compartment of COVID-19 associated deaths ( D ). The model equations read [ 19 , 39 ] where denotes the force of infection [ 29 ] or rate constant The model involves the parameters p , q , , , , , , , , , r , , , , , , , , , and , which are semi-positive. The parameters denote the probability of infection per contact ( p ), proportion of being quarantined ( q ), proportion of exposed who transition to ( ), proportion of exposed who transition to ( ), efficacy of quarantine ( ), general efficacy of quarantine ( ), quarantine rate of exposed ( ), incubation period of exposed ( ), incubation period of exposed ( ), isolation rate of ( ), proportion of exposed who transition to ( r ), rate of progression to ICU case ( ), death rate of non-isolated infectious ( ), death rate of isolated infectious ( ), death rate of asymptomatic cases ( ), death rate of ICU patients ( ), reduced infectiousness for asymptomatic cases ( ), reduced infectiousness for isolated cases …”

“…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 – 14 ]. In particular, it has been demonstrated that 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 – 19 ]. Such stage schemes in turn have been a key tool to understand COVID-19 waves and possible intervention impacts [ 20 – 26 ].…”