Critical properties of the susceptible-exposed-infected model on a square lattice

Wada, Alexander H. O.; Tomé, Tânia; Oliveira, Mário J. de

doi:10.1088/1742-5468/2015/04/p04014

Cited by 13 publications

(15 citation statements)

References 77 publications

(175 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Instead of writing down the master equation, which gives the time evolution of the probability distribution, we write the time evolution of some marginal probability distribution such as the one-site and two-site probability distributions. Using a procedure developed earlier [24,23] and the notations P X , P XY , P XY Z for one-site, two-site and three-site probabilities, the following time evolution equations can be derived…”

Section: First Modelmentioning

confidence: 99%

“…Again, using the procedure developed earlier [24,23], the following time evolution equations for the one-site and two-site probabilities can be obtained…”

Section: Second Modelmentioning

confidence: 99%

“…The stochastic model we use to generate clusters of site percolation is defined as follows [23,24]. Each site of a regular lattice is occupied by an individual that can be in one of three states: susceptible, exposed or immune.…”

Section: Introductionmentioning

confidence: 99%

“…The exposed and immune individuals remain forever in these states. Starting with a single exposed individual in a lattice full of susceptible individuals, a cluster of exposed individual is generated such that at the stationary state it is exactly mapped into a cluster of site percolation [23,24], with p being identified as the probability of a site occupation. Once a cluster of site percolation is generated by the model of spreading of disease explained above, we simulate the contact process in the top of the percolating cluster.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Critical properties of the contact process with quenched dilution

Wada¹,

Oliveira²

2017

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

Abstract.We have studied the critical properties of the contact process on a square lattice with quenched site dilution by Monte Carlo simulations. This was achieved by generating in advance the percolating cluster, through the use of an appropriate epidemic model, and then by the simulation of the contact process on the top of the percolating cluster. The dynamic critical exponents were calculated by assuming an activated scaling relation and the static exponents by the usual power law behavior. Our results are in agreement with the prediction that the quenched diluted contact process belongs to the universality class of the random transverse-field Ising model. We have also analyzed the model and determined the phase diagram by the use of a mean-field theory that takes into account the correlation between neighboring sites.

show abstract

Section: First Modelmentioning

confidence: 99%

“…Again, using the procedure developed earlier [24,23], the following time evolution equations for the one-site and two-site probabilities can be obtained…”

Section: Second Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Critical properties of the contact process with quenched dilution

Wada¹,

Oliveira²

2017

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Studies going in this direction are the ones of Ref. [16,[20][21][22]. However, despite the ABM allows a better flexibility of forms at microscopic level, and allows predicting the macroscopic behavior from simulations, this methodology does not allow a complete understanding of the underlying mechanisms of the system.…”

Section: Introductionmentioning

confidence: 99%

An attempt to unify some population growth models from first principles

Ribeiro

2016

Rev. Bras. Ensino Fís.

View full text Add to dashboard Cite

In this work, some phenomenological growth models based only on the population information (macroscopic level) are deduced in an intuitive way. These models, for instance Verhulst, Gompertz and Bertalanffy-Richards models, are introduced in such a way that all the parameters involved have a physical interpretation. A model based on the interaction (distance dependent) between the individuals (microscopic level) is also presented. This microscopic model have some phenomenological models as particular cases. In this approach, the Verhulst model represents the situation in which all the individuals interact in the same way, regardless of the distance between them (mean field approach). Other phenomenological models are retrieved from the microscopic model according to two quantities: i) the way that the interaction decays as a function the distance between two individuals and ii) the dimension of the spatial structure formed by the individuals of the population. This microscopic model allows understanding population growth by first principles, because it predicts that some phenomenological models can be seen as a consequence of interaction at individual level. The microscopic model discussed here paves the way to finding universal patterns that are common to all types of growth, even in systems of very different nature. Keywords: Population growth, Complex Systems, Mathematical Modelling Neste trabalho, alguns modelos fenomenológicos de crescimento populacional são deduzidos de uma forma intuitiva. Estes modelos, por exemplo os modelos de Verhulst, Gompertz e Bertalanffy-Richards, são introduzidos de maneira que todos os parâmetros envolvidos tenham uma interpretação física. Um modelo baseado na interação (dependente da distância) entre os indivíduos (nível microscópico) tambéḿ e apresentado.É mostrado que alguns modelos fenomenológicos são casos particulares deste modelo microscópico, de acordo com: i) a forma com que a interação competitiva entre indivíduos decai com a distância que os separam; e ii) a dimensão euclidiana da estrutura espacial formada pelos indivíduos da população. Nestas circunstâncias, o modelo de Verhulst, por exemplo, decorre quando todos os indivíduos interagem de forma independente da distância que os separam: uma situação tipo campo-médio. Este modelo microscópico permite compreender o crescimento populacional por primeiros princípios, uma vez que mostra que alguns modelos fenomenológicos são explicados a partir de interações no nível do indivíduo. Dessa forma, o modelo microscópico discutido aqui abre caminho para encontrar padrões universais que sejam comuns a todos os tipos de crescimento. Palavras-chave: Crescimento Populacional, Sistemas Complexos, Modelagem Matemática

show abstract

Stochastic Approach to Epidemic Spreading

Tomé

Oliveira

2020

Braz J Phys

Self Cite

View full text Add to dashboard Cite

We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition rates for each process such as infection or recovery are set up by using the law of mass action. We perform numerical simulations as well as numerical integration of the evolution equations for the average number of each class of individuals. The onset of the epidemic spreading is obtained by a linear analysis of the disease free state, from which follows the initial exponential increase of the infected and the frequency of new cases. The order parameter and the variance in the number of individuals are also obtained characterizing the onset of epidemic spreading as a critical phase transition.

show abstract

Critical properties of the susceptible-exposed-infected model on a square lattice

Cited by 13 publications

References 77 publications

Critical properties of the contact process with quenched dilution

Critical properties of the contact process with quenched dilution

An attempt to unify some population growth models from first principles

Stochastic Approach to Epidemic Spreading

Contact Info

Product

Resources

About