Epidemic Percolation Networks, Epidemic Outcomes, and Interventions

Epidemic percolation networks (EPNs) are directed random networks that can be used to analyze stochastic “Susceptible-Infectious-Removed” (SIR) and “Susceptible-Exposed-Infectious-Removed” (SEIR) epidemic models, unifying and generalizing previous uses of networks and branching processes to analyze mass-action and network-based S(E)IR models. This paper explains the fundamental concepts underlying the definition and use of EPNs, using them to build intuition about the final outcomes of epidemics. We then show how EPNs provide a novel and useful perspective on the design of vaccination strategies.

[1]  Aric Hagberg,et al.  Exploring Network Structure, Dynamics, and Function using NetworkX , 2008, Proceedings of the Python in Science Conference.

[2]  Anders Martin-Löf,et al.  Threshold limit theorems for some epidemic processes , 1980, Advances in Applied Probability.

[3]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[4]  Joseph Gani,et al.  Stochastic Epidemic Models and Their Statistical Analysis , 2002 .

[5]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[6]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[7]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[8]  O. Diekmann,et al.  Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation , 2000 .

[9]  Frank Ball,et al.  Poisson approximations for epidemics with two levels of mixing , 2004 .

[10]  M. Newman.  Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[12]  J. Robins,et al.  Second look at the spread of epidemics on networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Kari Kuulasmaa,et al.  The spatial general epidemic and locally dependent random graphs , 1982, Journal of Applied Probability.

[14]  Odo Diekmann,et al.  A deterministic epidemic model taking account of repeated contacts between the same individuals , 1998, Journal of Applied Probability.

[15]  Joel C. Miller,et al.  Epidemic size and probability in populations with heterogeneous infectivity and susceptibility. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Peter Donnelly,et al.  Strong approximations for epidemic models , 1995 .

[17]  Claude Lefèvre,et al.  A UNIFIED ANALYSIS OF THE FINAL SIZE AND SEVERITY DISTRIBUTION IN COLLECTIVE REED-FROST EPIDEMIC PROCESSES , 1990 .

[18]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[19]  Tutut Herawan,et al.  Computational and mathematical methods in medicine. , 2006, Computational and mathematical methods in medicine.

[20]  David G Kendall,et al.  Deterministic and Stochastic Epidemics in Closed Populations , 1956 .

[21]  Stan Zachary,et al.  On spàtial general epidemics and bond percolation processes , 1984, Journal of Applied Probability.

[22]  M E J Newman,et al.  Predicting epidemics on directed contact networks. , 2006, Journal of theoretical biology.

[23]  Donald Ludwig,et al.  Final size distribution for epidemics , 1975 .

[24]  S. N. Dorogovtsev,et al.  Giant strongly connected component of directed networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  James M Robins,et al.  Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing. , 2007, Journal of theoretical biology.

[26]  Håkan Andersson,et al.  Limit theorems for a random graph epidemic model , 1998 .

[27]  Joel C. Miller.  Bounding the Size and Probability of Epidemics on Networks , 2008, Journal of Applied Probability.