• Corpus ID: 17479960

Dynamical graphs for the SI epidemiological model

@article{Herrera2011DynamicalGF,
  title={Dynamical graphs for the SI epidemiological model},
  author={Jos{\'e} Luis Herrera and Gilberto C. Gonz{\'a}lez-Parra},
  journal={arXiv: Populations and Evolution},
  year={2011}
}
In this paper we study the susceptible-infectious (SI) epidemiological model using dynamical graphs. Dynamical structures have been recently applied in many areas including complex systems. Dynamical structures include the mutual interaction between the structure topology and the characteristics of its members. Dynamical graphs applied to epidemics consider generally that the nodes are individuals and the links represent different classes of relationships between individuals with the potential… 
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SHOWING 1-10 OF 19 REFERENCES

Adaptive Contact Networks Change Effective Disease Infectiousness and Dynamics

Disease dynamics in finite populations in which infection occurs along the links of a dynamical contact network whose reshaping may be biased based on each individual's health status are studied.

Simulations of infectious diseases on networks

Epidemic spreading in lattice-embedded scale-free networks

Modeling the effects of social impact on epidemic spreading in complex networks

Annealed and mean-field formulations of disease dynamics on static and adaptive networks.

By means of the annealed formulation of complex networks, a new heterogeneous mean-field formulation is derived that correctly reproduces the epidemic dynamics and accurately reproduce those obtained by extensive numerical simulations.

Equal Graph Partitioning on Estimated Infection Network as an Effective Epidemic Mitigation Measure

A proof-of-concept study demonstrating the effectiveness of epidemic mitigation based on estimated infection networks, by comparing it against traditional untargeted strategies, in slowing down and reducing the size of advancing epidemics.

A graph theoretical perspective of a drug abuse epidemic model

Epidemic spreading in real networks: an eigenvalue viewpoint

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.

The Mathematics of Infectious Diseases

Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.

Epidemic spreading in scale-free networks.

A dynamical model for the spreading of infections on scale-free networks is defined, finding the absence of an epidemic threshold and its associated critical behavior and this new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.