Analysis of the susceptible-infected-susceptible epidemic dynamics in networks via the non-backtracking matrix

  title={Analysis of the susceptible-infected-susceptible epidemic dynamics in networks via the non-backtracking matrix},
  author={Naoki Masuda and Masaki Ogura and Victor M. Preciado},
We study the stochastic susceptible-infected-susceptible model of epidemic processes on finite directed and weighted networks with arbitrary structure. We present a new lower bound on the exponential rate at which the probabilities of nodes being infected decay over time. This bound is directly related to the leading eigenvalue of a matrix that depends on the non-backtracking and incidence matrices of the network. The dimension of this matrix is $N+M$, where $N$ and $M$ are the number of… 

Figures from this paper

Effects of concurrency on epidemic spreading in Markovian temporal networks
The proposed theoretically tractable Markovian temporal network models, in which each edge flips between the active and inactive states in continuous time, are expected to be useful for investigating effects of concurrency on various collective dynamics on networks including both infectious and other dynamics.
Metzler/Zeta Correspondence
We present an explicit formula for the determinant on the Metzler matrix of a digraph D . Furthermore, we introduce a walk-type zeta function with respect to this Metzler matrix of the symmetric


Optimal Containment of Epidemics over Temporal Activity-Driven Networks
An adaptive model of epidemic processes is proposed, where the network topology dynamically changes due to both exogenous factors independent of the epidemic dynamics as well as endogenous preventive measures adopted by individuals in response to the state of the infection.
Thresholds for epidemic spreading in networks
It is conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.
Message passing approach for general epidemic models.
  • B. Karrer, M. Newman
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2010
A generalized version of the susceptible-infected-recovered model of epidemic disease that allows for arbitrary distributions of transmission and recovery times is studied and it is shown that the calculation gives a rigorous bound on the size of disease outbreaks.
Relevance of backtracking paths in recurrent-state epidemic spreading on networks
A modified recurrent-state dynamics is defined which explicitly forbids direct backtracking events and it is shown that this modification completely upsets the phenomenology.
Leveraging percolation theory to single out influential spreaders in networks
It is proved that the recently introduced nonbacktracking centrality is the optimal criterion for the identification of influential spreaders in locally tree-like networks at criticality and is a highly reliable metric to identify top influential spreader also in generic graphs not embedded in space and for noncritical spreading.
A message-passing approach for recurrent-state epidemic models on networks
This approach takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source, and thus avoids "echo chamber effects" where a pair of adjacent nodes each amplify the probability that the other is infectious.
Influence maximization in complex networks through optimal percolation
This work maps the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix of the network.
The effect of network topology on the spread of epidemics
  • A. Ganesh, L. Massoulié, D. Towsley
  • Mathematics, Computer Science
    Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies.
  • 2005
This paper identifies topological properties of the graph that determine the persistence of epidemics and shows that if the ratio of cure to infection rates is larger than the spectral radius of thegraph, then the mean epidemic lifetime is of order log n, where n is the number of nodes.
Percolation on sparse networks
Percolation is reformulate as a message passing process and the resulting equations can be used to calculate the size of the percolating cluster and the average cluster size, finding them to be highly accurate when compared with direct numerical simulations.
Networks and epidemic models
A variety of methods are described that allow the mixing network, or an approximation to the network, to be ascertained and how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control are suggested.