Mathematical Biosciences and Engineering (MBE)

Network-based analysis of a small Ebola outbreak
Pages: 67 - 77, Issue 1, February 2017

doi:10.3934/mbe.2017005      Abstract        References        Full text (742.2K)           Related Articles

Mark G. Burch - College of Public Health, The Ohio State University, Columbus, OH 43210, United States (email)
Karly A. Jacobsen - Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, United States (email)
Joseph H. Tien - Department of Mathematics and Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, United States (email)
Grzegorz A. Rempała - Mathematical Biosciences Institute and College of Public Health, The Ohio State University, Columbus, OH 43210, United States (email)

1 L. J. Allen, An introduction to stochastic epidemic models, Mathematical Epidemiology, Springer, 1945 (2008), 81-130.       
2 M. Altmann, The deterministic limit of infectious disease models with dynamic partners, Mathematical Biosciences, 150 (1998), 153-175.
3 H. Andersson and T. Britton, Stochastic Epidemic Models and Their Statistical Analysis, vol. 4, Springer New York, 2000.       
4 A. D. Barbour and G. Reinert, Approximating the epidemic curve, Electronic Journal of Probability, 18 (2013), 1-30.       
5 M. Boguñá, C. Castellano and R. Pastor-Satorras, Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks, Physical Review Letters, 111 (2013), 068701.
6 T. Bohman and M. Picollelli, SIR epidemics on random graphs with a fixed degree sequence, Random Structures & Algorithms, 41 (2012), 179-214.       
7 T. Britton and P. D. O'Neill, Bayesian inference for stochastic epidemics in populations with random social structure, Scandinavian Journal of Statistics, 29 (2002), 375-390.       
8 B. Choi and G. A. Rempala, Inference for discretely observed stochastic kinetic networks with applications to epidemic modeling, Biostatistics, 13 (2012), 153-165.
9 G. Chowell and H. Nishiura, Transmission dynamics and control of Ebola virus disease (EVD): A review, BMC Medicine, 12 (2014), p196.
10 L. Decreusefond, J.-S. Dhersin, P. Moyal and V. C. Tran et al., Large graph limit for an SIR process in random network with heterogeneous connectivity, The Annals of Applied Probability, 22 (2012), 541-575.       
11 C. Groendyke, D. Welch and D. R. Hunter, Bayesian inference for contact networks given epidemic data, Scandinavian Journal of Statistics, 38 (2011), 600-616.       
12 C. Groendyke, D. Welch and D. R. Hunter, A network-based analysis of the 1861 Hagelloch measles data, Biometrics, 68 (2012), 755-765.       
13 T. House and M. J. Keeling, Insights from unifying modern approximations to infections on networks, Journal of The Royal Society Interface, 8 (2011), 67-73.
14 S. Janson, M. Luczak and P. Windridge, Law of large numbers for the SIR epidemic on a random graph with given degrees, Random Structures & Algorithms, 45 (2014), 726-763.       
15 J. Janssen, Semi-Markov Models: Theory and Applications, Plenum Press, New York, 1986.       
16 M. Keeling, The implications of network structure for epidemic dynamics, Theoretical Population Biology, 67 (2005), 1-8.
17 M. J. Keeling, The effects of local spatial structure on epidemiological invasions, Proceedings of the Royal Society of London B: Biological Sciences, 266 (1999), 859-867.
18 M. Keeling, Correlation equations for endemic diseases: externally imposed and internally generated heterogeneity, Proceedings of the Royal Society of London B: Biological Sciences, 266 (1999), 953-960.
19 W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 115, The Royal Society, 1927, 700-721.
20 T. G. Kurtz, Limit theorems for sequences of jump markov processes approximating ordinary differential processes, Journal of Applied Probability, 8 (1971), 344-356.       
21 J. Legrand, R. Grais, P. Boelle, A. Valleron and A. Flahault, Understanding the dynamics of Ebola epidemics, Epidemiology and Infection, 135 (2007), 610-621.
22 G. D. Maganga, J. Kapetshi, N. Berthet, B. Kebela Ilunga, F. Kabange, P. Mbala Kingebeni, V. Mondonge, J.-J. T. Muyembe, E. Bertherat and S. Briand et al., Ebola virus disease in the democratic republic of congo, New England Journal of Medicine, 371 (2014), 2083-2091.
23 S. Meloni, N. Perra, A. Arenas, S. Gómez, Y. Moreno and A. Vespignani, Modeling human mobility responses to the large-scale spreading of infectious diseases, Scientific Reports, 1 (2011), 1-7.
24 J. C. Miller, A. C. Slim and E. M. Volz, Edge-based compartmental modelling for infectious disease spread, Journal of the Royal Society Interface, 9 (2012), 890-906.
25 J. C. Miller and E. M. Volz, Incorporating disease and population structure into models of SIR disease in contact networks, PloS One, 8 (2013), e69162.
26 M. Newman, Networks: An Introduction, Oxford University Press, 2010.       
27 L. Pellis, F. Ball, S. Bansal, K. Eames, T. House, V. Isham and P. Trapman, Eight challenges for network epidemic models, Epidemics, 10 (2015), 58-62.
28 D. Rand, Correlation equations and pair approximations for spatial ecologies, Advanced Ecological Theory: Principles and Applications, Oxford Blackwell Science, 1999.
29 E. J. Schwartz, B. Choi and G. A. Rempala, Estimating epidemic parameters: Application to H1N1 pandemic data, Math. Biosciences, 270 (2015), 198-203 (e-pub, ahead of print).       
30 W. E. R. Team, Ebola virus disease in west africa-the first 9 months of the epidemic and forward projections, N Engl J Med, 371 (2014), 1481-1495.
31 E. Volz, SIR dynamics in random networks with heterogeneous connectivity, Journal of Mathematical Biology, 56 (2008), 293-310.       
32 D. Welch, S. Bansal and D. R. Hunter, Statistical inference to advance network models in epidemiology, Epidemics, 3 (2011), 38-45.

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