# Transient Dynamics of Epidemic Spreading and Its Mitigation on Large Networks

@article{Lee2019TransientDO, title={Transient Dynamics of Epidemic Spreading and Its Mitigation on Large Networks}, author={Chul-Ho Lee and Srinivasarao Tenneti and Do Young Eun}, journal={Proceedings of the Twentieth ACM International Symposium on Mobile Ad Hoc Networking and Computing}, year={2019} }

In this paper, we aim to understand the transient dynamics of a susceptible-infected (SI) epidemic spreading process on a large network. The SI model has been largely overlooked in the literature, while it is naturally a better fit for modeling the malware propagation in early times when patches/vaccines are not available, or over a wider range of timescales when massive patching is practically infeasible. Nonetheless, its analysis is simply non-trivial, as its important dynamics are all…

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## References

SHOWING 1-10 OF 102 REFERENCES

Analysis of Exact and Approximated Epidemic Models over Complex Networks

- MathematicsArXiv
- 2016

This work provides a complete global analysis of the epidemic dynamics of the nonlinear mean-field approximation of the Markov chain model and shows that depending on the largest eigenvalue of the underlying graph adjacency matrix and the rates of infection, recovery, and vaccination, the global dynamics takes on one of two forms.

On the dynamics of deterministic epidemic propagation over networks

- Mathematics, Computer ScienceAnnu. Rev. Control.
- 2017

Thresholds for virus spread on networks

- Mathematicsvaluetools '06
- 2006

This work characterise how the size of the population that eventually becomes infected depends on the network topology, and shows that if the ratio of cure to infection rates is larger than the spectral radius of the graph, and the initial infected population is small, then the finalinfected population is also small in a sense that can be made precise.

Epidemic thresholds in real networks

- Computer ScienceTSEC
- 2008

A general epidemic threshold condition is proposed for the NLDS system: it is proved that the epidemic threshold for a network is exactly the inverse of the largest eigenvalue of its adjacency matrix, and it is shown that below the epidemic thresholds, infections die out at an exponential rate.

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 dynamics and endemic states in complex networks.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

A dynamical model for the spreading of epidemics in complex networks that implies that scale-free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess.

Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks

- Mathematics, Computer Science52nd IEEE Conference on Decision and Control
- 2013

A convex framework to find cost-optimal distribution of vaccination resources when different levels of vaccination are allowed is proposed to find the optimal distribution of vaccines throughout the network to control the spread of an epidemic outbreak.

Analysis and Control of Epidemics: A Survey of Spreading Processes on Complex Networks

- EducationIEEE Control Systems
- 2016

Various solved and open problems in the development, analysis, and control of epidemic models are reviewed and presented.

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.

Threshold Conditions for Arbitrary Cascade Models on Arbitrary Networks

- Computer ScienceIEEE ICDM 2011
- 2011

The G2-threshold (twice generalized) theorem is shown, which nicely de-couples the effect of the topology and the virus model and has broad implications for the vulnerability of real, complex networks, and numerous applications, including viral marketing, blog dynamics, influence propagation, easy answers to 'what-if' questions, and simplified design and evaluation of immunization policies.