Contact process with exogenous infection and the scaled SIS process

@article{Zhang2015ContactPW,
  title={Contact process with exogenous infection and the scaled SIS process},
  author={June Zhang and Jos{\'e} M. F. Moura},
  journal={J. Complex Networks},
  year={2015},
  volume={5},
  pages={712-733}
}
Propagation of contagion in networks depends on the graph topology. This paper is concerned with studying the time-asymptotic behavior of the extended contact processes on static, undirected, finite-size networks. This is a contact process with nonzero exogenous infection rate (also known as the {\epsilon}-SIS, {\epsilon} susceptible-infected-susceptible, model [1]). The only known analytical characterization of the equilibrium distribution of this process is for complete networks. For large… 
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References

SHOWING 1-10 OF 24 REFERENCES

Role of subgraphs in epidemics over finite-size networks under the scaled SIS process

It is proved that, for a range of epidemics parameters, this combinatorial problem leads to a submodular optimization problem, which is exactly solvable in polynomial time.

Accounting for topology in spreading contagion in non-complete networks

A continuous-time Markov chain infection model that explicitly accounts for the network topology, be it complete or non-complete, is offered and it is shown that network topologies have dramatic effect on the spread of infections.

Diffusion in Social Networks as SIS Epidemics: Beyond Full Mixing and Complete Graphs

The paper shows that interesting population asymptotic behaviors occur for scenarios where the individual tendencies of each agent oppose peer influences, and determines how the most probable configuration of agent states depends on both model parameters and network topology.

Threshold behavior of epidemics in regular networks

It is shown that for k-regular graph topologies, the most probable network state transitions from the state whereeveryone is healthy to one where everyone is infected at a threshold that depends on k but not on the size of the graph.

Epidemics in networks with nodal self-infection and the epidemic threshold.

An exact recursion relation for the Markov infinitesimal generator is presented and it is shown that for a certain range of small ε > 0, the in reality observed phase transition, also called the "metastable" state, that is characterized by the epidemic threshold is approximated.

Emergent behavior in large scale networks

It is shown that, under the heavy traffic assumption, the relevant underlying dynamics induces a coherent nontrivial metastable behavior in a macroscopic space-time scale: a slight imbalance on the effective spreading rate of one class over the others determines a significantly greater steady state predominance of this class overThe others, regardless of the initial distribution.

The effect of network topology on the spread of epidemics

  • A. GaneshL. MassouliéD. 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.

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.

Eight challenges for network epidemic models.

Dynamical Systems on Networks: A Tutorial

This tutorial should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks.