# Monte Carlo simulation and analytic approximation of epidemic processes on large networks

Open Mathematics (2013)

- Volume: 11, Issue: 4, page 800-815
- ISSN: 2391-5455

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topNoémi Nagy, and Péter Simon. "Monte Carlo simulation and analytic approximation of epidemic processes on large networks." Open Mathematics 11.4 (2013): 800-815. <http://eudml.org/doc/269800>.

@article{NoémiNagy2013,

abstract = {Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic spreads along the cycle graph as a front. We introduce a continuous time Markov chain describing the evolution of the front. The third method we apply is the subsystem approximation using the edges as subsystems. Finally, we compare the steady state value of the number of infected nodes obtained in different ways.},

author = {Noémi Nagy, Péter Simon},

journal = {Open Mathematics},

keywords = {SIS epidemic; ODE approximation; Network process; network process},

language = {eng},

number = {4},

pages = {800-815},

title = {Monte Carlo simulation and analytic approximation of epidemic processes on large networks},

url = {http://eudml.org/doc/269800},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Noémi Nagy

AU - Péter Simon

TI - Monte Carlo simulation and analytic approximation of epidemic processes on large networks

JO - Open Mathematics

PY - 2013

VL - 11

IS - 4

SP - 800

EP - 815

AB - Low dimensional ODE approximations that capture the main characteristics of SIS-type epidemic propagation along a cycle graph are derived. Three different methods are shown that can accurately predict the expected number of infected nodes in the graph. The first method is based on the derivation of a master equation for the number of infected nodes. This uses the average number of SI edges for a given number of the infected nodes. The second approach is based on the observation that the epidemic spreads along the cycle graph as a front. We introduce a continuous time Markov chain describing the evolution of the front. The third method we apply is the subsystem approximation using the edges as subsystems. Finally, we compare the steady state value of the number of infected nodes obtained in different ways.

LA - eng

KW - SIS epidemic; ODE approximation; Network process; network process

UR - http://eudml.org/doc/269800

ER -

## References

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