Epidemic phase and the site percolation with distant-neighbor interactions

Santos, C.B. dos; Barbin, Décio; Caliri, A.

doi:10.1016/s0375-9601(97)00889-x

Cited by 5 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If p 1 is the probability of infection due to one infected nearest neighbor, then (1− p 1 ) m is the probability of noninfection due to m infected nearest neighbors. Then the modified probability of infection [14] is…”

Section: Some Generalizationsmentioning

confidence: 99%

Phase Transitions in Some Epidemic Models Defined on Small-World Networks

Agiza

Elgazzar

Youssef

2003

Int. J. Mod. Phys. C

View full text Add to dashboard Cite

show abstract

Section: Some Generalizationsmentioning

confidence: 99%

Phase Transitions in Some Epidemic Models Defined on Small-World Networks

Agiza

Elgazzar

Youssef

2003

Int. J. Mod. Phys. C

View full text Add to dashboard Cite

show abstract

“…The probability p L as in the Eq. (3) [8], [6], and in a number of alternative forms [9], has been employed in the analogy between percolation and epidemic. Since that the critical value p c , in which random clusters grow to infinite size, is know (analytic or numerically) for any lattices, p c may be used as a powerful general criterion for 'epidemic spread' [10], [9].…”

Section: R 0 and The Threshold Phenomenonmentioning

confidence: 99%

“…(3) [8], [6], and in a number of alternative forms [9], has been employed in the analogy between percolation and epidemic. Since that the critical value p c , in which random clusters grow to infinite size, is know (analytic or numerically) for any lattices, p c may be used as a powerful general criterion for 'epidemic spread' [10], [9]. However, due to the traditional importance of the concept of R 0 in the epidemic scenario, this threshold is generalized for finite discrete systems, as described above, in order to show its relevance for an intrinsically individual based perspective of the problem.…”

Section: R 0 and The Threshold Phenomenonmentioning

confidence: 99%

Untitled

Alves¹,

Haas

Caliri

2003

Journal of Biological Physics

Self Cite

View full text Add to dashboard Cite

An important issue in theoretical epidemiology is the epidemic thresholdphenomenon, which specify the conditions for an epidemic to grow or die out.In standard (mean-field-like) compartmental models the concept of the basic reproductive number, R(0), has been systematically employed as apredictor for epidemic spread and as an analytical tool to study thethreshold conditions. Despite the importance of this quantity, there are nogeneral formulation of R(0) when one considers the spread of a disease ina generic finite population, involving, for instance, arbitrary topology ofinter-individual interactions and heterogeneous mixing of susceptible andimmune individuals. The goal of this work is to study this concept in ageneralized stochastic system described in terms of global and localvariables. In particular, the dependence of R(0) on the space ofparameters that define the model is investigated; it is found that near ofthe `classical' epidemic threshold transition the uncertainty about thestrength of the epidemic process still is significantly large. Theforecasting attributes of R(0) for a discrete finite system is discussedand generalized; in particular, it is shown that, for a discrete finitesystem, the pretentious predictive power of R(0) is significantlyreduced.

show abstract

“…The model considered here incorporates local and global variables that can be suitably balanced. It is treated by Monte Carlo (MC) simulation method and some relevant results are illustrated through especial density maps showing nuanced patterns, and epidemic phase diagrams (Santos et al, 1998).…”

Section: Introductionmentioning

confidence: 99%

Untitled

Haas

Caliri

Silva

1999

Journal of Biological Physics

Self Cite

View full text Add to dashboard Cite

The epidemic event, seen as a nonequilibrium dynamic process, is studied through a simple stochastic system reminiscent of the classical SIR model. The system is described in terms of global and local variables and was mainly treated by means of Monte Carlo simulation; square lattices N×N, with N=23, 51, 100, 151, and 211 were used. Distinct extensive runs were performed and then classified as corresponding to epidemic or non-epidemic phase. They were examined with detail through the analysis of the event duration and event size; illustrations, such as density-like plots in the space of the model's parameters, are provided. The epidemic/non-epidemic phase presents smaller/larger relative fluctuations, whereas closer to the threshold the uncertainty reaches its highest values. Far enough from the threshold, the distribution φ(t) of the events time duration t shows a step-like appearance. However at the threshold line it shows an exponential behavior of the form φ (t) ∼ exp (-ωt); the same behavior is observed for the event size distribution. These results help to explain why the approach to epidemic threshold would be hard to anticipate with standard census data.

show abstract

Epidemic phase and the site percolation with distant-neighbor interactions

Cited by 5 publications

References 9 publications

Phase Transitions in Some Epidemic Models Defined on Small-World Networks

Phase Transitions in Some Epidemic Models Defined on Small-World Networks

Untitled

Untitled

Contact Info

Product

Resources

About