# Delocalized epidemics on graphs: A maximum entropy approach

@article{Sahneh2016DelocalizedEO, title={Delocalized epidemics on graphs: A maximum entropy approach}, author={Faryad Darabi Sahneh and Aram Vajdi and Caterina M. Scoglio}, journal={2016 American Control Conference (ACC)}, year={2016}, pages={7346-7351} }

The susceptible-infected-susceptible (SIS) epidemic process on complex networks can show metastability, resembling an endemic equilibrium. In a general setting, the metastable state may involve a large portion of the network, or it can be localized on small subgraphs of the contact network. Localized infections are not interesting because a true outbreak concerns network-wide invasion of the contact graph rather than localized infection of certain sites within the contact network. Existing…

## 3 Citations

Metastable localization of diseases in complex networks.

- Computer SciencePhysical review. E
- 2016

We describe the phenomenon of localization in the epidemic susceptible-infective-susceptible model on highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers…

Network Localization Is Unalterable by Infections in Bursts

- Computer ScienceIEEE Transactions on Network Science and Engineering
- 2019

It is shown that the maximum near-threshold prevalence of the bursty SIS process on a localized network tends to zero even if <inline-formula><tex-math notation="LaTeX">$\lambda _1$</tex- math></inline- formula> diverges in the thermodynamic limit, which indicates that the burst of infection cannot turn a localized spreading into a delocalized spreading.

Spreading on Networks

- Computer Science
- 2019

This dissertation focuses on the analysis of a basic mathematical model of spreading phenomena running on underlying network structures and aims to complete the basic theory of spreading processes by exploring the Susceptible-Infected-Susceptible (SIS) model.

## References

SHOWING 1-10 OF 27 REFERENCES

Spectral analysis and slow spreading dynamics on complex networks.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

QMF results of SIS are compared with simulations on various large dimensional graphs and it is shown that for Erdős-Rényi graphs this method predicts correctly the occurrence of rare-region effects, and also provides a good estimate for the epidemic threshold in case of percolating graphs.

Epidemic spreading in real networks: an eigenvalue viewpoint

- Mathematics, Computer Science22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings.
- 2003

A general epidemic threshold condition that applies to arbitrary graphs is proposed and it is proved that, under reasonable approximations, the epidemic threshold for a network is closely related to the largest eigenvalue of its adjacency matrix.

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

- Mathematics
- 2013

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…

Stability properties of infection diffusion dynamics over directed networks

- Mathematics53rd IEEE Conference on Decision and Control
- 2014

It is proved that the endemic state is GAS in strongly connected networks when the graph is weakly connected, providing conditions for the existence, uniqueness, and global asymptotic stability of weak and strong endemic states.

The effect of network topology on the spread of epidemics

- Mathematics, Computer ScienceProceedings 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.

Epidemic phase transition of the SIS type in networks

- Mathematics
- 2012

By making only one approximation of a mean-eld type, this work determines the nature of the SIS type of epidemic phase transition in any network: the steady-state fraction of infected nodes y∞ is linear in c and the derivative at the epidemic thresholdc= 1 �1 is exactly computed.

The N-intertwined SIS epidemic network model

- Computer ScienceComputing
- 2011

The N-intertwined virus spread model of the SIS-type is introduced as a promising and analytically tractable model of which the steady-state behavior is fairly completely determined and much insight can be gained that is hidden in the exact Markov model.

Generalized Epidemic Mean-Field Model for Spreading Processes Over Multilayer Complex Networks

- Computer Science, MathematicsIEEE/ACM Transactions on Networking
- 2013

A detailed description of the stochastic process at the agent level where the agents interact through different layers, each represented by a graph is provided, including spreading of virus and information in computer networks and spreading of multiple pathogens in a host population.

Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks.

- MathematicsPhysical review letters
- 2013

We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks.…

Susceptible-infected-susceptible model: a comparison of N-intertwined and heterogeneous mean-field approximations.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This work focuses on the epidemic threshold and the steady-state fraction of infected nodes in networks with different degree distributions and concludes that the N-intertwined approximation is superior to the HMF approximation in regular graphs.