scholarly journals How can contemporary climate research help understand epidemic dynamics? Ensemble approach and snapshot attractors

2020 ◽  
Vol 17 (173) ◽  
pp. 20200648
Author(s):  
T. Kovács
Keyword(s):  
Complex Dynamics ◽  
Internal Variability ◽  
Climate Change Research ◽  
Contact Parameter ◽  
Epidemic Dynamics ◽  
Ensemble Approach ◽  
Statistical Measures ◽  
Trajectory Representation ◽  
Parameter Values ◽  
Contemporary Climate

Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed upon a monotonic decay needs a different description from that of the standard chaotic dynamics. The concept of snapshot attractors and their natural distribution has been adopted from the field of the latest climate change research. This shows the importance of the finite-time chaotic effect and ensemble interpretation while investigating the spread of a disease. By defining statistical measures over the ensemble, we can interpret the internal variability of the epidemic as the onset of complex dynamics—even for those values of contact parameters where originally regular behaviour is expected. We argue that anomalous outbreaks of the infectious class cannot die out until transient chaos is presented in the system. Nevertheless, this fact becomes apparent by using an ensemble approach rather than a single trajectory representation. These findings are applicable generally in explicitly time-dependent epidemic systems regardless of parameter values and time scales.

Information content of data with respect to models

1983 ◽  
Vol 245 (5) ◽  
pp. R620-R623
Author(s):  
M. Berman ◽  
P. Van Eerdewegh
Keyword(s):  
Experimental Data ◽  
Data Collection ◽  
Information Content ◽  
Mathematical Framework ◽  
Statistical Measures ◽  
Parameter Values ◽  
Collection Strategies

A measure is proposed for the information content of data with respect to models. A model, defined by a set of parameter values in a mathematical framework, is considered a point in a hyperspace. The proposed measure expresses the information content of experimental data as the contribution they make, in units of information bits, in defining a model to within a desired region of the hyperspace. This measure is then normalized to conventional statistical measures of uncertainty. It is shown how the measure can be used to estimate the information of newly planned experiments and help in decisions on data collection strategies.

scholarly journals The Give and Take Game: Analysis of a Resource Sharing Game

2015 ◽  
Vol 25 (4) ◽  
pp. 753-767 ◽  
Author(s):  
Pedro Mariano ◽  
Luís Correia
Keyword(s):  
Resource Sharing ◽  
Nash Equilibria ◽  
Complex Dynamics ◽  
Pareto Optimal ◽  
Game Analysis ◽  
Multiple Strategies ◽  
Multi Stage ◽  
Depth Analysis ◽  
Simple Rules ◽  
Parameter Values

AbstractWe analyseGive and Take, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and durable resource, and in each stage players may either do nothing or, depending on their roles, give the resource or take it. Despite these simple rules, we show that this game has interesting complex dynamics. Unique toGive and Takeis the existence of multiple Pareto optimal profiles that can also be Nash equilibria, and a built-in punishment action. This game allows us to study cooperation in sharing an indivisible and durable resource. Since there are multiple strategies to cooperate,Give and Takeprovides a base to investigate coordination under implicit or explicit agreements. We discuss its position in face of other games and real world situations that are better modelled by it. The paper presents an in-depth analysis of the game for the range of admissible parameter values. We show that, when taking is costly for both players, cooperation emerges as players prefer to give the resource.

scholarly journals Performance of early warning signals for disease emergence: a case study on COVID-19 data

2021 ◽  
Author(s):  
Daniele Proverbio ◽  
Françoise Kemp ◽  
Stefano Magni ◽  
Jorge Gonçalves
Keyword(s):  
Early Warning ◽  
Disease Emergence ◽  
Warning Signals ◽  
Active Monitoring ◽  
Prevalence Data ◽  
Early Warning Signals ◽  
Epidemic Dynamics ◽  
Critical Transitions ◽  
Parameter Values

AbstractThe sudden emergence of infectious diseases pose threats to societies worldwide and it is notably difficult to detect. In the past few years, several early warning signals (EWS) were introduced, to alert to impending critical transitions and extend the set of indicators for risk assessment. While they were originally thought to be generic, recent works demonstrated their sensitivity to some dynamical characteristics such as system noise and rates of approach to critical parameter values. Moreover, testing on empirical data is so far limited. Hence, validating their performance remains a challenge. In this study, we analyse the performance of common EWS such as increasing variance and autocorrelation in detecting the emergence of COVID-19 outbreaks in various countries, based on prevalence data. We show that EWS are successful in detecting disease emergence provided that some basic assumptions are satisfied: a slow forcing through the transitions and not fat-tailed noise. We also show cases where EWS fail, thus providing a verification analysis of their potential and limitations. Overall, this suggests that EWS can be useful for active monitoring of epidemic dynamics, but that their performance is sensitive to surveillance procedures. Our results thus represent a further step towards the application of EWS indicators for informing public health policies.

scholarly journals How Should Cancer Models Be Constructed?

2020 ◽  
Vol 27 (1) ◽  
pp. 107327482096200
Author(s):  
Robert A. Beckman ◽  
Irina Kareva ◽  
Frederick R. Adler
Keyword(s):  
Complex Dynamics ◽  
Full Range ◽  
Evolutionary Game ◽  
Treatment Strategies ◽  
Predator Prey ◽  
Cancer Models ◽  
The Face ◽  
Predator Prey Models ◽  
The Right ◽  
Parameter Values

Choosing and optimizing treatment strategies for cancer requires capturing its complex dynamics sufficiently well for understanding but without being overwhelmed. Mathematical models are essential to achieve this understanding, and we discuss the challenge of choosing the right level of complexity to address the full range of tumor complexity from growth, the generation of tumor heterogeneity, and interactions within tumors and with treatments and the tumor microenvironment. We discuss the differences between conceptual and descriptive models, and compare the use of predator-prey models, evolutionary game theory, and dynamic precision medicine approaches in the face of uncertainty about mechanisms and parameter values. Although there is of course no one-size-fits-all approach, we conclude that broad and flexible thinking about cancer, based on combined modeling approaches, will play a key role in finding creative and improved treatments.

scholarly journals Host-Parasitoid Model With Intraspecific Competitions

2012 ◽  
Vol 1 (2) ◽  
pp. 105
Author(s):  
Banshidhar Sahoo ◽  
Swarup Poria
Keyword(s):  
Discrete Time ◽  
Bifurcation Analysis ◽  
Complex Dynamics ◽  
Handling Time ◽  
Phase Portraits ◽  
Search Rate ◽  
Reasonable Range ◽  
Different Types ◽  
Oscillatory Coexistence ◽  
Parameter Values

In this paper a discrete-time host-parasitoid model with intraspecific competitions is proposed. Phase portraits are drawn for different types of intraspecific competitions to notice the effects of intraspecific competitions for biologically reasonable range of parameter values. Bifurcation analysis is done with respect to instantaneous search rate as well as handling time for different types of intraspecific competitions. Many forms of complex dynamics such as chaos, periodic windows etc. are observed. The stable coexistence as well as oscillatory coexistence of host and parasitoid are shown under different types of intraspecific competitions. The Hopf point and attractor crises exist for different intraspecific competitions.

scholarly journals Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics

2020 ◽  
Vol 378 (2173) ◽  
pp. 20190388 ◽  
Author(s):  
Matthew J. Hoffman ◽  
Elizabeth M. Cherry
Keyword(s):  
Data Assimilation ◽  
Temporal Dynamics ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Model Error ◽  
Model Parameters ◽  
Ensemble Spread ◽  
Spatio Temporal ◽  
System States ◽  
Parameter Values

Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm’s sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble. This article is part of the theme issue ‘Uncertainty quantification in cardiac and cardiovascular modelling and simulation’.

Dynamics of a Leslie-Gower predator-prey system with hunting cooperation and prey harvesting

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yong Yao ◽  
Lingling Liu
Keyword(s):  
Complex Dynamics ◽  
Critical Values ◽  
Predator Population ◽  
Predator Prey ◽  
Codimension Two ◽  
Prey System ◽  
Constant Rate ◽  
Risk Of Extinction ◽  
Parameter Values ◽  
Theoretical Results

<p style='text-indent:20px;'>In this paper, we study the dynamics of a Leslie-Gower predator-prey system with hunting cooperation among predator population and constant-rate harvesting for prey population. It is shown that there are a weak focus of multiplicity up to three and a cusp of codimension at most two for various parameter values, and the system exhibits two saddle-node bifurcations, a Bogdanov-Takens bifurcation of codimension two and a Hopf bifurcation as the bifurcation parameters vary. The results developed in this article reveal far more complex dynamics compared to the Leslie-Gower system and show how the prey harvesting and the hunting cooperation affect the dynamics of the system. In particular, there exist some critical values of prey harvesting and hunting cooperation such that the predator and prey populations are at risk of extinction if the intensities of harvesting and hunting cooperation are greater than these critical values. Moreover, numerical simulations are presented to illustrate our theoretical results.</p>

COMPLEX DYNAMICS OF BILINEAR OSCILLATOR CLOSE TO GRAZING

2010 ◽  
Vol 20 (11) ◽  
pp. 3801-3817 ◽  
Author(s):  
EKATERINA PAVLOVSKAIA ◽  
JAMES ING ◽  
MARIAN WIERCIGROCH ◽  
SOUMITRO BANERJEE
Keyword(s):  
Complex Dynamics ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Basins Of Attraction ◽  
Experimental Investigations ◽  
Unstable Periodic Orbits ◽  
Chaotic Oscillations ◽  
Impact Oscillator ◽  
Parameter Values ◽  
Elastic Constraint

In this work the strange behavior of an impact oscillator with a one-sided elastic constraint discovered experimentally is compared with the predictions obtained using its mathematical model. Extensive experimental investigations undertaken on the rig developed at the Aberdeen University reveal different bifurcation scenarios under varying excitation frequency near grazing which were recorded for a number of values of the excitation amplitude. In the paper, particular attention is paid to the chaotic oscillations recorded near grazing frequency when a nonimpacting orbit becomes an impacting one under increasing excitation frequency. It was found that the evolution of the attractor is governed by a complex interplay between smooth and nonsmooth bifurcations, and the interactions between a number of coexisting orbits. The occurrence of coexisting attractors is manifested in the experimental results through discontinuous transitions from one orbit to another via boundary crisis. In some cases, the basins of attraction have a fractal structure. Detailed numerical exploration also revealed coexisting unstable periodic orbits. These stable and unstable coexisting orbits are often born far from the parameter values at which they influence the system dynamics. The very rich dynamics of the bilinear oscillator close to grazing is demonstrated and typical mechanisms of the attractors' appearance and disappearance are explained using stability analysis.

scholarly journals Complex dynamics of a three species food-chain model with Holling type IV functional response

2011 ◽  
Vol 16 (3) ◽  
pp. 553-374
Author(s):  
Ranjit Kumar Upadhyay ◽  
Sharada Nandan Raw
Keyword(s):  
Food Chain ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Chain Model ◽  
Narrow Region ◽  
Type Iv ◽  
Numerical Bifurcation ◽  
Parameter Values ◽  
Food Chain Model

In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence criterion of the food chain model is obtained. Numerical bifurcation analysis reveals the chaotic behavior in a narrow region of the bifurcation parameter space for biologically realistic parameter values of the model system. Transition to chaotic behavior is established via period-doubling bifurcation and some sequences of distinctive period-halving bifurcation leading to limit cycles are observed.

scholarly journals Analysis of the Effect of Mass Parameters on Motorcycle Vibration and Stability

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5090
Author(s):  
Andrzej Dębowski
Keyword(s):  
Torsional Vibration ◽  
Vibration Analysis ◽  
Complex Dynamics ◽  
Steering System ◽  
The Other ◽  
Vibration Frequencies ◽  
Analysis Method ◽  
Resonant Frequencies ◽  
Vehicle Weight ◽  
Parameter Values

This paper presents a vibration analysis method and an example of its application to evaluate the influence of mass parameters on torsional vibration frequencies in the steering system of a motorcycle. The purpose of this paper is to analyze to what extent vibration frequencies can change during their daily operation. These changes are largely due to the ratio of vehicle weight to driver and load. The complex dynamics make it very difficult to conduct research using simple models. It is difficult to observe the influence of individual parameters because they are strongly interrelated. This paper provides a description of the vibration analysis method, and the results are presented in the form of Bode diagrams and tables. On this basis, it was found that the driver, deciding on the way of using the vehicle and introducing modifications in it, influences the resonant frequencies of the steering system. Typical exploitation factors, on the other hand, do not cause significant changes, although they may contribute to increasing the sensitivity of the system to vibrations. The conducted analysis also showed some nonlinear changes in the dynamics of the system with linear changes of the parameter values.

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