Dynamic transitions in small world networks: Approach to equilibrium limit

Gade, Prashant M.; Sinha, Sudeshna

doi:10.1103/physreve.72.052903

Cited by 36 publications

(30 citation statements)

References 16 publications

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“…From these observations, we suggested that these patterns were determined by competition be- * E-mail: garuda@skku.edu tween the typical life cycle of the disease and the time taken by it to go around the world [22]. This proposition is consistent with the remark by Gade and Sinha [21] that the time scales are quite important. Roxin et al [9] in this spirit even though they treated a neuron system.…”

Section: Introductionsupporting

confidence: 81%

“…The interacting element can be a nonlinear oscillator [5][6][7], an excitable neuron [8][9][10][11], a biological species [12,13], a sand pile [14][15][16], an epidemic disease [17][18][19][20][21][22][23], or even a game participant [24][25][26]. These approaches help one to analyze various aspects of this world, including biology, sociology, politics, and economy, as well as the physics itself [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

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Oscillatory Behaviors of an Epidemiological Model on Small-World Networks

Ki¹

2007

J. Korean Phys. Soc.

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We investigate the oscillatory dynamics of an epidemiological model of SIRS(susceptible-infectiverecovered-susceptible) type on small-world networks. A delay differential equation for the infected population is derived to show that three characteristic patterns, stationarity, oscillation, and synchronized extermination exist, depending on the competition between the disease's life cycle and the time for it to sweep the world. Numerical calculations support this prediction and suggest that the synchronization parameter proposed by Kuramoto can be a good measure of patterns.

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Section: Introductionsupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Oscillatory Behaviors of an Epidemiological Model on Small-World Networks

Ki¹

2007

J. Korean Phys. Soc.

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“…In the modeling of many interacting particles on the networks, the effect of the networks structure on the properties of dynamical systems defined on such networks has been attracted a lot of attention recently, and researchers from fields ranging from neurodynamics and ecology to social sciences have been extensively working in this area [1,2,3,4,5,6,7,8]. In small world networks [6], one starts with a ring of N nodes, in which each node connected to its k nearest neighbors on either side.…”

Section: Introductionmentioning

confidence: 99%

Epidemic threshold for the SIRS model on the networks

Saif

2019

Physica A: Statistical Mechanics and its Applications

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We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on small world network. We show the effects of all the parameters associated with this model on small world network and we create the full phase space. The results we obtained are consistent with those obtained in Ref. [7] in terms of the existence of a phase transition from a fluctuating endemic state to self-sustained oscillations in the size of the infected subpopulation at a finite value of the disorder of the network. And also our results assert that, that transition specifically occurs where the average clusterization shifts from high to low. The effect of clustering coefficient on SIRS model on the networks can be understood from the results obtained in Ref. [9], which indicates the importance of existing the loops in the network, in order to the disease to spread frequently throughout the nodes of network. where, clusters tend to spread infection among close-knit neighborhoods. Hence, when the loops are high inside the network, the reinfection occurs in the network at many places and at different times, which looks like as a kind of randomness in occurring the second period of infection. Whereas when the number of loops are low, reinfection occurs at specific places and times on the network, which looks like as a kind of regularity in occurring the second period of infection.

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“…Therefore, we added sources of infection in the model, i.e. a limited number of infective individuals remain in this state all the time [8].…”

Section: Numerical Calculationsmentioning

confidence: 99%

When will the Covid-19 epidemic fade out?

Renna

2020

Preprint

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A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behaviour observed in the incidence of real infectious diseases. For this purpose, we analyse a SIRS model under the framework of a small world network formulation. Using this model, we make predictions about the peak of the Covid-19 epidemic in Italy. A Gaussian fit is also performed, to make a similar prediction.

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Dynamic transitions in small world networks: Approach to equilibrium limit

Cited by 36 publications

References 16 publications

Oscillatory Behaviors of an Epidemiological Model on Small-World Networks

Oscillatory Behaviors of an Epidemiological Model on Small-World Networks

Epidemic threshold for the SIRS model on the networks

When will the Covid-19 epidemic fade out?

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