COVID-19 ORDER PARAMETERS AND ORDER PARAMETER TIME CONSTANTS OF ITALY AND CHINA: A MODELING APPROACH BASED ON SYNERGETICS

2020 ◽  
Vol 28 (03) ◽  
pp. 589-608 ◽  
Author(s):  
T. D. FRANK
Keyword(s):  
Dynamical Systems ◽  
Compartment Model ◽  
Order Parameters ◽  
Unstable State ◽  
Human Populations ◽  
Time Constants ◽  
Systems Perspective ◽  
Infection Dynamics ◽  
Model Spaces ◽  
Systems Framework

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.

A Dynamical Systems Perspective on Music

1997 ◽  
Vol 15 (4) ◽  
pp. 529-545
Author(s):  
David Burrows
Keyword(s):  
Dynamical Systems ◽  
Systems Perspective

scholarly journals Modeling Epidemic Spread among a Commuting Population Using Transport Schemes

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1861
Author(s):  
Daniela Calvetti ◽  
Alexander P. Hoover ◽  
Johnie Rose ◽  
Erkki Somersalo
Keyword(s):  
Network Model ◽  
Transport Theory ◽  
Optimal Transport ◽  
State Level ◽  
Compartment Model ◽  
Census Bureau ◽  
Mitigation Strategies ◽  
Mitigation Measures ◽  
Metapopulation Model ◽  
Infection Dynamics

Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two.

Correlations Between Hysteretic Categorical and Continuous Judgments of Perceptual Stimuli Supporting a Unified Dynamical Systems Approach to Perception

Perception ◽  
2017 ◽  
Vol 47 (1) ◽  
pp. 44-66 ◽  
Author(s):  
S. Kim ◽  
T. D. Frank
Keyword(s):  
Dynamical Systems ◽  
Systems Approach ◽  
Brain Activity ◽  
Equation Model ◽  
Measurement Scale ◽  
Systems Perspective ◽  
Within Subjects ◽  
Scale Measure ◽  
Positive Correlations ◽  
Experimental Findings

We report from two variants of a figure-ground experiment that is known in the literature to involve a bistable perceptual domain. The first variant was conducted as a two-alternative forced-choice experiment and in doing so tested participants on a categorical measurement scale. The second variant involved a Likert scale measure that was considered to represent a continuous measurement scale. The two variants were conducted as a single within-subjects experiment. Measures of bistability operationalized in terms of hysteresis size scores showed significant positive correlations across the two response conditions. The experimental findings are consistent with a dualistic interpretation of self-organizing perceptual systems when they are described on a macrolevel by means of so-called amplitude equations. This is explicitly demonstrated for a Lotka–Volterra–Haken amplitude equation model of task-related brain activity. As a by-product, the proposed dynamical systems perspective also sheds new light on the anchoring problem of producing numerical, continuous judgments.

Emergence of critical climate states during the Pleistocene

2021 ◽  
Author(s):  
Nicholas Golledge
Keyword(s):  
Dynamical Systems ◽  
Late Pleistocene ◽  
Dominant Frequency ◽  
Climate System ◽  
Ice Age ◽  
Early Pleistocene ◽  
Glacial Cycles ◽  
Pleistocene Climate ◽  
System Nodes ◽  
Systems Framework

<p>During the Pleistocene (approximately 2.6 Ma to present) glacial to interglacial climate variability evolved from dominantly 40 kyr cyclicity (Early Pleistocene) to 100 kyr cyclicity (Late Pleistocene to present). Three aspects of this period remain poorly understood: Why did the dominant frequency of climate oscillation change, given that no major changes in orbital forcing occurred? Why are the longer glacial cycles of the Late Pleistocene characterised by a more asymmetric form with abrupt terminations? And how can the Late Pleistocene climate be controlled by 100 kyr cyclicity when astronomical forcings of this frequency are so much weaker than those operating on shorter periods? Here we show that the decreasing frequency and increasing asymmetry that characterise Late Pleistocene ice age cycles both emerge naturally in dynamical systems in response to increasing system complexity, with collapse events (terminations) occuring only once a critical state has been reached. Using insights from network theory we propose that evolution to a state of criticality involves progressive coupling between climate system 'nodes', which ultimately allows any component of the climate system to trigger a globally synchronous termination. We propose that the climate state is synchronised at the 100 kyr frequency, rather than at shorter periods, because eccentricity-driven insolation variability controls mean temperature change globally, whereas shorter-period astronomical forcings only affect the spatial pattern of thermal forcing and thus do not favour global synchronisation. This dynamical systems framework extends and complements existing theories by accomodating the differing mechanistic interpretations of previous studies without conflict.</p>

scholarly journals The effect of seasonal birth pulses on pathogen persistence in wild mammal populations

2014 ◽  
Vol 281 (1786) ◽  
pp. 20132962 ◽  
Author(s):  
A. J. Peel ◽  
J. R. C. Pulliam ◽  
A. D. Luis ◽  
R. K. Plowright ◽  
T. J. O'Shea ◽  
...  
Keyword(s):  
Communicable Disease ◽  
Mammalian Species ◽  
Human Populations ◽  
Community Size ◽  
Closed Population ◽  
Birth Pulse ◽  
Infection Dynamics ◽  
Pathogen Persistence ◽  
Host Life ◽  
Parameter Ranges

The notion of a critical community size (CCS), or population size that is likely to result in long-term persistence of a communicable disease, has been developed based on the empirical observations of acute immunizing infections in human populations, and extended for use in wildlife populations. Seasonal birth pulses are frequently observed in wildlife and are expected to impact infection dynamics, yet their effect on pathogen persistence and CCS have not been considered. To investigate this issue theoretically, we use stochastic epidemiological models to ask how host life-history traits and infection parameters interact to determine pathogen persistence within a closed population. We fit seasonal birth pulse models to data from diverse mammalian species in order to identify realistic parameter ranges. When varying the synchrony of the birth pulse with all other parameters being constant, our model predicted that the CCS can vary by more than two orders of magnitude. Tighter birth pulses tended to drive pathogen extinction by creating large amplitude oscillations in prevalence, especially with high demographic turnover and short infectious periods. Parameters affecting the relative timing of the epidemic and birth pulse peaks determined the intensity and direction of the effect of pre-existing immunity in the population on the pathogen's ability to persist beyond the initial epidemic following its introduction.

scholarly journals A random dynamical systems perspective on stochastic resonance

Nonlinearity ◽  
2017 ◽  
Vol 30 (7) ◽  
pp. 2835-2853 ◽  
Author(s):  
Anna Maria Cherubini ◽  
Jeroen S W Lamb ◽  
Martin Rasmussen ◽  
Yuzuru Sato
Keyword(s):  
Dynamical Systems ◽  
Stochastic Resonance ◽  
Random Dynamical Systems ◽  
Systems Perspective

scholarly journals The Shallow Cognitive Map Hypothesis: A Hippocampal framework for Thought Disorder in Schizophrenia

2021 ◽  
Author(s):  
Ayesha Musa ◽  
Safia Khan ◽  
Minahil Mujahid ◽  
Mohamady
Keyword(s):  
Dynamical Systems ◽  
Cognitive Mapping ◽  
Cognitive Maps ◽  
Cognitive Map ◽  
Thought Disorder ◽  
Cellular Mechanisms ◽  
Relational Knowledge ◽  
Psychological Theories ◽  
Major Chemical ◽  
Systems Framework

Memories are not formed in isolation. They are associated and organized into relational knowledge structures that allow coherent thought. Failure to express such coherent thought is a key hallmark of Schizophrenia. Here we explore the hypothesis that thought disorder arises from disorganized Hippocampal cognitive maps. In doing so, we combine insights from two key lines of investigation, one concerning the neural signatures of cognitive mapping, and another that seeks to understand lower-level cellular mechanisms of cognition within a dynamical systems framework. Specifically, we propose that multiple distinct pathological pathways converge on the shallowing of Hippocampal attractors, giving rise to disorganized Hippocampal cognitive maps and driving thought disorder. We discuss the available evidence at the computational, behavioural, network and cellular levels. We also outline testable predictions from this framework including how it could unify major chemical and psychological theories of schizophrenia and how it can provide a rationale for understanding the aetiology and treatment of the disease.

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