INFLUENCE OF THE INITIAL SOURCE OF EPIDEMIC AND PREVENTIVE VACCINATION ON THE SPREADING PHENOMENA IN A TWO-DIMENSIONAL LATTICE

2004 ◽  
Vol 15 (06) ◽  
pp. 755-765 ◽  
Author(s):  
R. A. KOSIŃSKI ◽  
Ł. ADAMOWSKI
Keyword(s):  
Long Range ◽  
Probabilistic Model ◽  
Small World ◽  
Two Dimensional ◽  
Small World Networks ◽  
Spreading Process ◽  
Dimensional Lattice ◽  
Epidemic Curve ◽  
Preventive Vaccination ◽  
Initial Source

The probabilistic model of epidemic in a two-dimensional lattice with an additional random, long range connections characteristic for the small world networks is presented. Relations describing the spreading process of epidemics, like epidemic curve or range of epidemic in time, were found. The influence of the borders of the lattice and the localization of the initial source of epidemic on the epidemic curve is found analytically. The application of the preventive vaccination in the population is discussed.

Fractal aggregation on small-world networks with long-range deposition

Fractals ◽  
2020 ◽  
Author(s):  
Ren-Fei Wang ◽  
Sheng-Jun Wang ◽  
Zi-Gang Huang
Keyword(s):  
Long Range ◽  
Small World ◽  
Small World Networks

EXISTENCE, COST AND ROBUSTNESS OF SPATIAL SMALL-WORLD NETWORKS

2007 ◽  
Vol 17 (07) ◽  
pp. 2331-2342 ◽  
Author(s):  
P. DE LOS RIOS ◽  
T. PETERMANN
Keyword(s):  
Euclidean Space ◽  
Long Range ◽  
Communication Systems ◽  
Large Scale ◽  
Probability Distributions ◽  
Flow Distribution ◽  
Small World ◽  
Electronic Circuits ◽  
Small World Networks ◽  
Network Cost

Small-world networks embedded in Euclidean space represent useful cartoon models for a number of real systems such as electronic circuits, communication systems, the large-scale brain architecture and others. Since the small-world behavior relies on the presence of long-range connections that are likely to have a cost which is a growing function of the length, we explore whether it is possible to choose suitable probability distributions for the shortcut lengths so as to preserve the small-world feature and, at the same time, to minimize the network cost. The flow distribution for such networks, and their robustness, are also investigated.

scholarly journals Asymptotic Behaviour of Gossip Processes and Small-World Networks

2013 ◽  
Vol 45 (4) ◽  
pp. 981-1010 ◽  
Author(s):  
A. D. Barbour ◽  
G. Reinert
Keyword(s):  
Long Range ◽  
Branching Process ◽  
Small World ◽  
Random Variable ◽  
Random Networks ◽  
Small World Networks ◽  
Transmission Of Information ◽  
Characteristic Behaviour ◽  
Typical Distances ◽  
Common Behaviour

Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.

scholarly journals Asymptotic Behaviour of Gossip Processes and Small-World Networks

2013 ◽  
Vol 45 (04) ◽  
pp. 981-1010 ◽  
Author(s):  
A. D. Barbour ◽  
G. Reinert
Keyword(s):  
Long Range ◽  
Branching Process ◽  
Small World ◽  
Random Variable ◽  
Random Networks ◽  
Small World Networks ◽  
Transmission Of Information ◽  
Characteristic Behaviour ◽  
Typical Distances ◽  
Common Behaviour

Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.

scholarly journals Efficient routeing in Poisson small-world networks

2006 ◽  
Vol 43 (3) ◽  
pp. 678-686 ◽  
Author(s):  
M. Draief ◽  
A. Ganesh
Keyword(s):  
Point Process ◽  
Network Model ◽  
Poisson Point Process ◽  
Continuum Model ◽  
Small World ◽  
Small World Network ◽  
Small World Networks ◽  
Dimensional Lattice ◽  
Fixed Radius

In a recent paper, Kleinberg (2000) considered a small-world network model consisting of a d-dimensional lattice augmented with shortcuts. The probability of a shortcut being present between two points decays as a power, r-α, of the distance, r, between them. Kleinberg showed that greedy routeing is efficient if α = d and that there is no efficient decentralised routeing algorithm if α ≠ d. The results were extended to a continuum model by Franceschetti and Meester (2003). In our work, we extend the result to more realistic models constructed from a Poisson point process wherein each point is connected to all its neighbours within some fixed radius, and possesses random shortcuts to more distant nodes as described above.

scholarly journals Three-state majority-vote model on small-world networks

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Bernardo J. Zubillaga ◽  
André L. M. Vilela ◽  
Minggang Wang ◽  
Ruijin Du ◽  
Gaogao Dong ◽  
...  
Keyword(s):  
Social Interactions ◽  
Social Order ◽  
Majority Vote ◽  
Small World ◽  
Opinion Dynamics ◽  
Clustering Coefficient ◽  
Square Lattice ◽  
Two Dimensional ◽  
Small World Networks ◽  
Vote Model

AbstractIn this work, we study the opinion dynamics of the three-state majority-vote model on small-world networks of social interactions. In the majority-vote dynamics, an individual adopts the opinion of the majority of its neighbors with probability 1-q, and a different opinion with chance q, where q stands for the noise parameter. The noise q acts as a social temperature, inducing dissent among individual opinions. With probability p, we rewire the connections of the two-dimensional square lattice network, allowing long-range interactions in the society, thus yielding the small-world property present in many different real-world systems. We investigate the degree distribution, average clustering coefficient and average shortest path length to characterize the topology of the rewired networks of social interactions. By employing Monte Carlo simulations, we investigate the second-order phase transition of the three-state majority-vote dynamics, and obtain the critical noise $$q_c$$ q c , as well as the standard critical exponents $$\beta /\nu$$ β / ν , $$\gamma /\nu$$ γ / ν , and $$1/\nu$$ 1 / ν for several values of the rewiring probability p. We conclude that the rewiring of the lattice enhances the social order in the system and drives the model to different universality classes from that of the three-state majority-vote model in two-dimensional square lattices.

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