Finite size effects in epidemic spreading: the problem of overpopulated systems

Open Physics ◽  
2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Wojciech Ganczarek
Keyword(s):  
Mixing Time ◽  
Finite Size ◽  
Network Size ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Time Step ◽  
Finite Size Effects ◽  
Sexually Transmitted ◽  
The Impact ◽  
Quasi Stationary Distribution

AbstractIn this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.

scholarly journals Nonlocal and Size-Dependent Dielectric Function for Plasmonic Nanoparticles

2019 ◽  
Vol 9 (15) ◽  
pp. 3083
Author(s):  
Kai-Jian Huang ◽  
Shui-Jie Qin ◽  
Zheng-Ping Zhang ◽  
Zhao Ding ◽  
Zhong-Chen Bai
Keyword(s):  
Metallic Nanoparticles ◽  
High Efficiency ◽  
Finite Size ◽  
Plasmonic Nanostructures ◽  
Accurate Analysis ◽  
Finite Size Effects ◽  
Size Dependent ◽  
Quantum Size ◽  
The Impact ◽  
Electron Energy Loss

We develop a theoretical approach to investigate the impact that nonlocal and finite-size effects have on the dielectric response of plasmonic nanostructures. Through simulations, comprehensive comparisons of the electron energy loss spectroscopy (EELS) and the optical performance are discussed for a gold spherical dimer system in terms of different dielectric models. Our study offers a paradigm of high efficiency compatible dielectric theoretical framework for accounting the metallic nanoparticles behavior combining local, nonlocal and size-dependent effects in broader energy and size ranges. The results of accurate analysis and simulation for these effects unveil the weight and the evolution of both surface and bulk plasmons vibrational mechanisms, which are important for further understanding the electrodynamics properties of structures at the nanoscale. Particularly, our method can be extended to other plasmonic nanostructures where quantum-size or strongly interacting effects are likely to play an important role.

scholarly journals Epidemic Spreading with Heterogeneous Awareness on Human Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Yanling Lu ◽  
Guoping Jiang ◽  
Zhengxin Wang
Keyword(s):  
Theoretical Analysis ◽  
Epidemic Model ◽  
Arrival Time ◽  
Behavioral Responses ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Epidemic Dynamics ◽  
Awareness Information ◽  
The Impact ◽  
Human Networks

The spontaneous awareness behavioral responses of individuals have a significant impact on epidemic spreading. In this paper, a modified Susceptible-Alert-Infected-Susceptible (SAIS) epidemic model with heterogeneous awareness is presented to study epidemic spreading in human networks and the impact of heterogeneous awareness on epidemic dynamics. In this model, when susceptible individuals receive awareness information about the presence of epidemic from their infected neighbor nodes, they will become alert individuals with heterogeneous awareness rate. Theoretical analysis and numerical simulations show that heterogeneous awareness can enhance the epidemic threshold with certain conditions and reduce the scale of virus outbreaks compared with no awareness. What is more, for the same awareness parameter, it also shows that heterogeneous awareness can slow effectively the spreading size and does not delay the arrival time of epidemic spreading peak compared with homogeneous awareness.

Joint effect of individual’s memory and attractiveness in temporal network on spreading dynamics

2019 ◽  
Vol 30 (01) ◽  
pp. 1950011 ◽  
Author(s):  
Mei Yang ◽  
Bing Wang ◽  
Yuexing Han
Keyword(s):  
Network Model ◽  
Joint Effect ◽  
Network Evolution ◽  
Disease Spread ◽  
Temporal Network ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Modeling Framework ◽  
Positive Correlations ◽  
The Impact

Most real networks have been found to evolve dynamically. In addition, heterogeneity of interaction strengths and individual’s memory have been proved to be important to affect network evolution in the area of complex networks. Based on a recent extension of the activity-driven modeling framework, i.e. activity-driven model with attractiveness, where individuals are characterized by their activities and attractiveness, we propose a new temporal network model by considering individuals’ memory. Similar to the previous network model, we also investigate heterogeneous distributions and different correlations between the two variables (activity and attractiveness). By numerical simulations, we illustrate the impact of memory on epidemic spreading processes unfolding on the proposed model. We find that, when individuals’ attractiveness is fixed, memory does not cause dramatic change on the epidemic threshold in the SIR process, but it inhibits the epidemic spreading by reducing the infected ratio. While for the SIS process, in the case of uncorrelated and positive correlations between the two variables, memory facilitates the epidemic outbreaks by shrinking the epidemic threshold. When the two variables are negatively correlated, memory does not take obvious impact on the epidemic threshold. Besides, for the two processes unfolding on the network with and without memory, the propagation threshold decreases with the enhancement of the positive correlation, however, it almost does not get much influence from the negative correlation strength. It indicates that for the individuals with same activity, more attractive individuals will promote the disease spread. The findings deepen our understanding of the role of individuals’ memory and their attractiveness in the epidemic spreading process.

Finite-size effects on semi-directed Barabási–Albert networks

2016 ◽  
Vol 27 (09) ◽  
pp. 1650109 ◽  
Author(s):  
M. A. Radwan ◽  
Muneer A. Sumour ◽  
A. M. Elbitar ◽  
M. M. Shabat ◽  
F. W. S. Lima
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Finite Size ◽  
Network Size ◽  
Finite Size Effect ◽  
Finite Size Effects ◽  
Scale Free ◽  
Number Formula

In scale-free Barabási–Albert (BA) networks, we study the finite-size effect at different number m of neighbors. So, we investigate the effects of finite network size N for the recently developed semi-directed BA networks (SDBA1 and SDBA2) at fixed [Formula: see text]) and show and explain the gap in the distribution of the number [Formula: see text] of neighbors of the nodes i.

scholarly journals The Impact of the Global and Local Awareness Diffusion on Epidemic Transmission Considering the Heterogeneity of Individual Influences

2022 ◽  
Author(s):  
Haidong Xu ◽  
Ye Zhao ◽  
Dun Han
Keyword(s):  
Mean Field ◽  
Global Awareness ◽  
Protective Behavior ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Spreading Model ◽  
Information Layer ◽  
Local Awareness ◽  
Global And Local ◽  
The Impact

Abstract In this paper, we propose a coupled awareness - epidemic spreading model considering the heterogeneity of individual influences, which aims to explore the interaction between awareness diffusion and epidemic transmission. The considered heterogeneity of individual influences are threefold: the heterogeneity of individual influences in the information layer, the heterogeneity of individual influences in the epidemic layer and the heterogeneity of individual behavioral responses to epidemics. In addition, the individuals' receptive preference for information and the impacts of individuals' perceived local awareness ratio and individuals' perceived epidemic severity on self-protective behavior are included. The epidemic threshold is theoretically established according to the microscopic Markov chain approach and mean-field approach. Results indicate that the critical local and global awareness ratios have two-stage effects on the epidemic threshold. Besides, either the heterogeneity of individual influences in the information layer or the strength of individuals' responses to epidemics can influence the epidemic threshold with a nonlinear way. However, the heterogeneity of individual influences in the epidemic layer has few effect on the epidemic threshold, but can affects the magnitude of the final infected density.

scholarly journals Self-Awareness-Based Resource Allocation Strategy for Containment of Epidemic Spreading

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaolong Chen ◽  
Quanhui Liu ◽  
Ruijie Wang ◽  
Qing Li ◽  
Wei Wang
Keyword(s):  
Resource Allocation ◽  
Network Structure ◽  
Coupled Model ◽  
Tuning Parameter ◽  
Self Awareness ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Optimal Point ◽  
Allocation Model ◽  
The Impact

Resource support between individuals is of particular importance in controlling or mitigating epidemic spreading, especially during pandemics. However, there remains the question of how we can protect ourselves from being infected while helping others by donating resources in fighting against the epidemic. To answer the question, we propose a novel resource allocation model by considering the awareness of self-protection of individuals. In the model, a tuning parameter is introduced to quantify the reaction strength of individuals when they are aware of the disease. And then, a coupled model of resource allocation and disease spreading is proposed to study the impact of self-awareness on resource allocation and its impact on the dynamics of epidemic spreading. Through theoretical analysis and extensive Monte Carlo simulations, we find that in the stationary state, the system converges to two states: the whole healthy or the completely infected, which indicates an abrupt increase in the prevalence when there is a shortage of resources. More importantly, we find that too cautious and too selfless for the people during the outbreak of an epidemic are both not suitable for disease control. Through extensive simulations, we locate the optimal point, at which there is a maximum value of the epidemic threshold, and an outbreak can be delayed to the greatest extent. At last, we study further the effects of the network structure on the coupled dynamics. We find that the degree heterogeneity promotes the outbreak of disease, and the network structure does not alter the optimal phenomenon in behavior response. Based on the results of this study, a constructive suggestion is that in the face of a global pandemic, individuals or countries should strengthen mutual support and cooperation while doing their own prevention to suppress the epidemic optimally.

scholarly journals A lattice calculation of the hadronic vacuum polarization contribution to (g – 2)µ

2018 ◽  
Vol 175 ◽  
pp. 06031 ◽  
Author(s):  
M. Della Morte ◽  
A. Francis ◽  
A. Gérardin ◽  
V. Gülpers ◽  
G. Herdoíza ◽  
...  
Keyword(s):  
Finite Size ◽  
Pion Form Factor ◽  
Lattice Calculation ◽  
Muon Anomalous Magnetic Moment ◽  
Long Distance ◽  
Finite Size Effects ◽  
Polarization Contribution ◽  
Vector Channel ◽  
Vacuum Polarisation ◽  
The Impact

We present results of calculations of the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment. Specifically, we focus on controlling the infrared regime of the vacuum polarisation function. Our results are corrected for finite-size effects by combining the Gounaris-Sakurai parameterisation of the timelike pion form factor with the Lüscher formalism. The impact of quark-disconnected diagrams and the precision of the scale determination is discussed and included in our final result in two-flavour QCD, which carries an overall uncertainty of 6%. We present preliminary results computed on ensembles with Nf = 2 + 1 dynamical flavours and discuss how the long-distance contribution can be accurately constrained by a dedicated spectrum calculation in the iso-vector channel.

scholarly journals A stochastic-statistical residential burglary model with independent Poisson clocks

2020 ◽  
Vol 32 (1) ◽  
pp. 32-58
Author(s):  
CHUNTIAN WANG ◽  
YUAN ZHANG ◽  
ANDREA L. BERTOZZI ◽  
MARTIN B. SHORT
Keyword(s):  
Pattern Formation ◽  
Statistical Model ◽  
Finite Size ◽  
Residential Burglary ◽  
Time Step ◽  
Finite Size Effects ◽  
Agent Based ◽  
Stochastic Component ◽  
Active Particles ◽  
First Time

Residential burglary is a social problem in every major urban area. As such, progress has been to develop quantitative, informative and applicable models for this type of crime: (1) the Deterministic-time-step (DTS) model [Short, D’Orsogna, Pasour, Tita, Brantingham, Bertozzi & Chayes (2008) Math. Models Methods Appl. Sci.18, 1249–1267], a pioneering agent-based statistical model of residential burglary criminal behaviour, with deterministic time steps assumed for arrivals of events in which the residential burglary aggregate pattern formation is quantitatively studied for the first time; (2) the SSRB model (agent-based stochastic-statistical model of residential burglary crime) [Wang, Zhang, Bertozzi & Short (2019) Active Particles, Vol. 2, Springer Nature Switzerland AG, in press], in which the stochastic component of the model is theoretically analysed by introduction of a Poisson clock with time steps turned into exponentially distributed random variables. To incorporate independence of agents, in this work, five types of Poisson clocks are taken into consideration. Poisson clocks (I), (II) and (III) govern independent agent actions of burglary behaviour, and Poisson clocks (IV) and (V) govern interactions of agents with the environment. All the Poisson clocks are independent. The time increments are independently exponentially distributed, which are more suitable to model individual actions of agents. Applying the method of merging and splitting of Poisson processes, the independent Poisson clocks can be treated as one, making the analysis and simulation similar to the SSRB model. A Martingale formula is derived, which consists of a deterministic and a stochastic component. A scaling property of the Martingale formulation with varying burglar population is found, which provides a theory to the finite size effects. The theory is supported by quantitative numerical simulations using the pattern-formation quantifying statistics. Results presented here will be transformative for both elements of application and analysis of agent-based models for residential burglary or in other domains.

scholarly journals Optimal Control Strategy for Traffic Driven Epidemic Spreading Based on Community Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fei Shao ◽  
Guo-Ping Jiang
Keyword(s):  
Community Structure ◽  
Control Strategy ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Optimal Control Strategy ◽  
Scale Free ◽  
Second Moments ◽  
Scale Free Networks ◽  
Novel Strategy ◽  
The Impact

It is shown that community structure has a great impact on traffic transportation and epidemic spreading. The density of infected nodes and the epidemic threshold have been proven to have significant relationship with the node betweenness in traffic driven epidemic spreading method. In this paper, considering the impact of community structure on traffic driven epidemic spreading, an effective and novel strategy to control epidemic spreading in scale-free networks is proposed. Theoretical analysis shows that the new control strategy will obviously increase the ratio between the first and the second moments of the node betweenness distribution in scale-free networks. It is also found that the more accurate the community is identified, the stronger community structure the network has and the more efficient the control strategy is. Simulations on both computer-generated and real-world networks have confirmed the theoretical results.

scholarly journals Novel insights in the Levy–Levy–Solomon agent-based economic market model

2020 ◽  
pp. 2150020
Author(s):  
Maximilian Beikirch ◽  
Torsten Trimborn
Keyword(s):  
Size Effects ◽  
Random Number Generator ◽  
Finite Size ◽  
Market Model ◽  
Economic Market ◽  
Finite Size Effects ◽  
Agent Based ◽  
Huge Impact ◽  
Economic Market Model ◽  
The Impact

The Levy–Levy–Solomon (LLS) model [M. Levy, H. Levy and S. Solomon, Econ. Lett.45, 103 (1994)] is one of the most influential agent-based economic market models. In several publications this model has been discussed and analyzed. Especially Lux and Zschischang [E. Zschischang and T. Lux, Physica A: Stat. Mech. Appl.291, 563 (2001)] have shown that the model exhibits finite-size effects. In this study, we extend existing work in several directions. First, we show simulations which reveal finite-size effects of the model. Second, we shed light on the origin of these finite-size effects. Furthermore, we demonstrate the sensitivity of the LLS model with respect to random numbers. Especially, we can conclude that a low-quality pseudo-random number generator has a huge impact on the simulation results. Finally, we study the impact of the stopping criteria in the market clearance mechanism of the LLS model.

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