Reactivating dynamics for the susceptible-infected-susceptible model: a simple method to simulate the absorbing phase

Filho, Antônio de Pádua Ferreira da Silva; Alves, G. A.; Filho, R. N. Costa; Alves, T. F. A.

doi:10.1088/1742-5468/aab04a

Cited by 11 publications

(11 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that there is a complete branch of literature whose concern is the efficient sampling of the quasistationary distribution of states for processes with an absorbing state, such as the SIS model (see Refs. [37,[49][50][51] for instance). Indeed, finite size analysis of the critical phenomenon requires the sampling of sequences that do not fall on the absorbing state.…”

Section: Discussionmentioning

confidence: 99%

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm

St-Onge

Young

Dubé

2019

Computer Physics Communications

View full text Add to dashboard Cite

Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require O(log N ) or even O(1) operations per update-where N is the number of nodes-display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations on large networks. To circumvent the issue, we propose a node-based method combined with a composition and rejection algorithm, a sampling scheme that has an average-case complexity of O[log(log N )] per update for general networks. This systematic approach is first set-up for Markovian dynamics, but can also be adapted to a number of non-Markovian processes and can enhance considerably the study of a wide range of dynamics on networks.

show abstract

Section: Discussionmentioning

confidence: 99%

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm

St-Onge

Young

Dubé

2019

Computer Physics Communications

View full text Add to dashboard Cite

show abstract

“…• Reactivation method [39,40]: If there is no infected node in the entire network, we increase N r by one unit, and we randomly infect one node of the network to continue the simulation. Effects of reactivation on the stationary state can be measured by the reactivating field h r = Nr N t which is the average of inserted particles (i.e., spontaneously infected individuals) and scales as 1/N in the absorbing phase, vanishing in the thermodynamic limit;…”

Section: Reactivation Of the Dynamicsmentioning

confidence: 99%

Phase Diagram of the Contact Process on Barabasi-Albert Networks

Alencar¹,

Alves²,

Alves³

et al. 2022

Preprint

View full text Add to dashboard Cite

We show results for the contact process on Barabasi networks. The contact process is a model for an epidemic spreading without permanent immunity that has an absorbing state. For finite lattices, the absorbing state is the true stationary state, which leads to the need for simulation of quasi-stationary states, which we did in two ways: reactivation by inserting spontaneous infected individuals, or by the quasi-stationary method, where we store a list of active states to continue the simulation when the system visits the absorbing state. The system presents an absorbing phase transition where the critical behavior obeys the Mean Field exponents β = 1, γ = 0, and ν = 2. However, the different quasi-stationary states present distinct finite-size logarithmic corrections. We also report the critical thresholds of the model as a linear function of the network connectivity inverse 1/z, and the extrapolation of the critical threshold function for z → ∞ yields the basic reproduction number R 0 = 1 of the complete graph, as expected. Decreasing the network connectivity leads to the increase of the critical basic reproduction number R 0 for this model.

show abstract

“…Reactivation step: The simulation time is then updated by a time unit. If there is no infected individual in the entire network, we increase N r by one unit, and we randomly select one node of the network and turn all of its susceptible to infected ones in order to continue the simulation [8];…”

Section: B Modified Diffusive Epidemic Process and Implementationmentioning

confidence: 99%

“…Based on this, we report that epidemic processes have been widely studied over the last years, for instance, by the physicists' community. Thus, many models were created and applied to mimic and to understand such epidemic processes, including the Susceptible-Infected-Susceptible (SIS) model [5][6][7][8], Susceptible-Infected-Recovered (SIR) model [9][10][11],…”

Section: Introductionmentioning

confidence: 99%

Modified Epidemic Diffusive Process on the Apollonian Network

Alencar¹,

Macedo-Filho²,

Alves³

et al. 2021

Preprint

View full text Add to dashboard Cite

We present an analysis of an epidemic spreading process on the Apollonian network that can describe an epidemic spreading in a non-sedentary population. The modified diffusive epidemic process was employed in this analysis in a computational context by means of the Monte Carlo method. Our model has been useful for modeling systems closer to reality consisting of two classes of individuals: susceptible (A) and infected (B). The individuals can diffuse in a network according to constant diffusion rates D A and D B , for the classes A and B, respectively, and obeying three diffusive regimes, i.

show abstract

Reactivating dynamics for the susceptible-infected-susceptible model: a simple method to simulate the absorbing phase

Cited by 11 publications

References 27 publications

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm

Phase Diagram of the Contact Process on Barabasi-Albert Networks

Modified Epidemic Diffusive Process on the Apollonian Network

Contact Info

Product

Resources

About