Second-order mean-field susceptible-infected-susceptible epidemic threshold

Cator, Eric; Mieghem, Piet Van

doi:10.1103/physreve.85.056111

Cited by 110 publications

(116 citation statements)

References 15 publications

Supporting

Mentioning

113

Contrasting

Unclassified

Order By: Relevance

“…, in line with the fact that the N -intertwined mean-field approximation upper bounds the viral node probability [14]. For large N and small ε * τ so that ( ε * τ +j ) j !…”

Section: Scaling Of the Epidemic Thresholdmentioning

confidence: 67%

See 1 more Smart Citation

Epidemics in networks with nodal self-infection and the epidemic threshold

Mieghem

Cator²

2012

Phys. Rev. E

125

View full text Add to dashboard Cite

Since the Susceptible-Infected-Susceptible (SIS) epidemic threshold is not precisely defined in spite of its practical importance, the classical SIS epidemic process has been generalized to the ε−SIS model, where a node possesses a self-infection rate ε, in addition to a link infection rate β and a curing rate δ. The exact Markov equations are derived, from which the steady state can be computed. The major advantage of the ε−SIS model is that its steady state is different from the absorbing (or overall-healthy state) and approximates, for a certain range of small ε > 0, the in reality observed phase transition, also called the "metastable" state, that is characterized by the epidemic threshold. The exact steady-state analysis for the complete graph illustrates the effect of small ε and the quality of the first-order mean-field approximation, the N -intertwined model, proposed earlier. Apart from duality principles, often used in the mathematical literature, we present an exact recursion relation for the Markov infinitesimal generator.

show abstract

“…, in line with the fact that the N -intertwined mean-field approximation upper bounds the viral node probability [14]. For large N and small ε * τ so that ( ε * τ +j ) j !…”

Section: Scaling Of the Epidemic Thresholdmentioning

confidence: 67%

“…Higher order mean-field approximations have been derived in Ref. [14] illustrating the existence of a sequence of more accurate lower bounds…”

Section: Introductionmentioning

confidence: 99%

Epidemics in networks with nodal self-infection and the epidemic threshold

Mieghem

Cator²

2012

Phys. Rev. E

125

View full text Add to dashboard Cite

show abstract

“…[4,8]). Since X i is a Bernoulli random variable with the nice property that E½X i ¼ Pr½X i ¼ 1 , the exact SIS governing equation [3] for node i equalswhere (1) also holds for asymmetric adjacency matrices. In some of our previously published work, where undirected graphs (i.e., A ¼ A T ) were assumed, A must in some cases be replaced by its transpose A T in the equations in order to be valid for directed graphs.…”

mentioning

confidence: 99%

“…Since X i is a Bernoulli random variable with the nice property that E½X i ¼ Pr½X i ¼ 1 , the exact SIS governing equation [3] for node i equals…”

mentioning

confidence: 99%

“…[1][2][3][4][5][6][7]) much effort has been devoted to the precise computation of the epidemic threshold in the continuous-time susceptible-infected-susceptible (SIS) Markov model in networks. In that simple SIS model, the viral state of a node i at time t is specified by a Bernoulli random variable X i ðtÞ 2 f0; 1g: X i ðtÞ ¼ 0 for a healthy node and X i ðtÞ ¼ 1 for an infected node.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks

2013

Self Cite

View full text Add to dashboard Cite

Most studies on susceptible-infected-susceptible epidemics in networks implicitly assume Markovian behavior: the time to infect a direct neighbor is exponentially distributed. Much effort so far has been devoted to characterize and precisely compute the epidemic threshold in susceptible-infected-susceptible Markovian epidemics on networks. Here, we report the rather dramatic effect of a nonexponential infection time (while still assuming an exponential curing time) on the epidemic threshold by considering Weibullean infection times with the same mean, but different power exponent . For three basic classes of graphs, the Erdős-Rényi random graph, scale-free graphs and lattices, the average steady-state fraction of infected nodes is simulated from which the epidemic threshold is deduced. For all graph classes, the epidemic threshold significantly increases with the power exponents . Hence, real epidemics that violate the exponential or Markovian assumption can behave seriously differently than anticipated based on Markov theory. The epidemic threshold of a network distinguishes between the overall-healthy network regime and the effective infection regime where permanently a nonzero fraction of the nodes is infected. The epidemic threshold reflects the effectivity of an epidemic in a particular network and is a major indicator or tool to protect the nodes (people, computers, etc.) and to take preventive measures (governmental immunization strategies, antivirus software protection).Recently (see, e.g., Refs. [1][2][3][4][5][6][7]) much effort has been devoted to the precise computation of the epidemic threshold in the continuous-time susceptible-infected-susceptible (SIS) Markov model in networks. In that simple SIS model, the viral state of a node i at time t is specified by a Bernoulli random variable X i ðtÞ 2 f0; 1g: X i ðtÞ ¼ 0 for a healthy node and X i ðtÞ ¼ 1 for an infected node. A node i at time t can be in one of two states: infected, with probability v i ðtÞ ¼ Pr½X i ðtÞ ¼ 1 or healthy, with probability 1 À v i ðtÞ, but susceptible to the infection. The curing process per node i is a Poisson process with rate and the infection rate per link is a Poisson process with rate . Obviously, only when a node is infected, can it infect its direct neighbors that are still healthy. Both the curing and infection Poisson processes are independent. The network is represented by an adjacency matrix A, where a ij ¼ 1 if there is a link from node i to node j, otherwise a ij ¼ 0. A major complication in the SIS Markov model is the absorbing state to which the epidemic SIS process always converges after a sufficiently long time in any network G with a finite number N of nodes and L of links. Hence, the steady state is the overall-healthy (absorbing) state. Since the exact steady state is physically less meaningful, the epidemic threshold refers to the metastable or quasistationary state which is observed in practice. However, the metastable state needs to be defined (see, e.g., Refs. [4,8]).Since X i is a Bernoulli random ...

show abstract

Receding Horizon Control on the Broadcast of Information in Stochastic Networks

Silva,

Shen,

et al. 2024

Springer Proceedings in Advanced Robotics

View full text Add to dashboard Cite

Second-order mean-field susceptible-infected-susceptible epidemic threshold

Cited by 110 publications

References 15 publications

Epidemics in networks with nodal self-infection and the epidemic threshold

Epidemics in networks with nodal self-infection and the epidemic threshold

Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks

Receding Horizon Control on the Broadcast of Information in Stochastic Networks

Contact Info

Product

Resources

About