Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC

Authors

  • Boseung Choi Department of National Statistics, Korea University Sejoung Campus, Seoul, Republic of Korea
  • Sydney Busch Augsburg University
  • Dieudonne Kazadi Ministry of Health, Democratic Republic of Kongo, Kinshasa, DRC
  • Benoit Kebela Department of Public Health, University of Kinshasa, Kinshasa, DRC
  • Emile Okitolonda Department of Public Health, University of Kinshasa, Kinshasa, DRC
  • Yi Dai Division of Biostatistics, The Ohio State University
  • Robert M Lumpkin Department of Statistics, The Ohio State University
  • Wasiur Rahman Khuda Bukhsh Mathematical Biosciences Institute, The Ohio State University
  • Omar Saucedo Mathematical Biosciences Institute, The Ohio State University
  • Marcel Yotebieng Division of Epidemiology The Ohio State University
  • Joe Tien Department of Mathematics The Ohio State University
  • Eben B Kenah Division of Biostatistics The Ohio State University
  • Grzegorz A Rempala Department of Mathematics, Division of Biostatistics and Mathematical Biosciences Institute, The Ohio State University http://orcid.org/0000-0002-6307-4555

DOI:

https://doi.org/10.11145/j.biomath.2019.10.037

Keywords:

parameter estimation, branching process, Markov Chain Monte-Carlo methods, survival dynamical system

Abstract

We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach isВ based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused byВ Bundibugyo ebolavirusВ in city of Isiro, Demo- cratic Republic of the Congo. The branching process model allows for a direct comparison of disease transmission across different environments, such as the general community or the Ebola treatment unit. However, the survival model appears to yield parameter estimates with more accuracy and better precision in some circumstances.

Author Biography

Grzegorz A Rempala, Department of Mathematics, Division of Biostatistics and Mathematical Biosciences Institute, The Ohio State University

Professorof Mathematics and Biostatistics, Former Interim Director, В Mathematical Biosciences Institute

References

The World Health Orgtanization, “Ebola virus disease in Democratic Republic of the Congo, May 2018,” https://www.who.int/csr/don/30-may-2018-ebola-drc/en/.

H. Andersson and T. Britton, Stochastic epidemic models and their statistical analysis. Springer Science & Business Media, 2012, vol. 151.

D. Brockmann and D. Helbing, “The hidden geometry of complex, network-driven contagion phenomena,” Science, vol. 342, no. 6164, pp. 1337–1342, 2013.

P. S. Dodds and D. J. Watts, “Universal behavior in a gener- alized model of contagion,” Physical Review Letters, vol. 92, no. 21, pp. 218 701(1) – 218 201(4), 2004.

T. House and M. J. Keeling, “Insights from unifying modern approximations to infections on networks,” Journal of The Royal Society Interface, vol. 8, no. 54, pp. 67–73, 2011.

L.A.Meyers,B.Pourbohloul,M.E.Newman,D.M.Skowron- ski, and R. C. Brunham, “Network theory and SARS: predicting outbreak diversity,” Journal of Theoretical Biology, vol. 232, pp. 71–81, 2005.

E.Volz,“SIRdynamicsinrandomnetworkswithheterogeneous connectivity,” Journal of Mathematical Biology, vol. 56, no. 3, pp. 293–310, 2008.

J. C. Miller and E. M. Volz, “Incorporating disease and popula- tion structure into models of SIR disease in contact networks,” PLoS One, vol. 8, no. 8, p. e69162, 2013.

I. Z. Kiss, J. C. Miller, and P. L. Simon, Mathematics of epidemics on networks: from exact to approximate models. Springer, 2017, vol. 46.

W. R. KhudaBukhsh, B. Choi, E. Kenah, and G. A. Rempala, “Survival dynamical systems for the population-level analysis of epidemics,” arXiv preprint arXiv:1901.00405, 2019.

K. J. Olival and D. T. Hayman, “Filoviruses in bats: current knowledge and future directions,” Viruses, vol. 6, no. 4, pp. 1759–1788, 2014.

K. M. Johnson, J. V. Lange, P. A. Webb, and F. A. Murphy, “Isolation and partial characterisation of a new virus causing acute haemorrhagic fever in Zaire,” Lancet, vol. 309, no. 8011, pp. 569–571, 1977.

The Centers for Disease Control and Prevention (CDC), “Out- breaks chronology: Ebola virus disease 2014,” http://www. cdc.gov/vhf/ebola/outbreaks/history/chronology.html.

G. D. Maganga, J. Kapetshi, N. Berthet, B. Kebela Ilunga, F. Kabange, P. Mbala Kingebeni, V. Mondonge, J.-J. T. Muyembe, E. Bertherat, S. Briand et al., “Ebola virus disease in the Democratic Republic of Congo,” New England Journal of Medicine, vol. 371, no. 22, pp. 2083–2091, 2014.

C. E. M. Coltart, A. M. Johnson, and C. J. M. Whitty, “Role of healthcare workers in early epidemic spread of Ebola: policy implications of prophylactic compared to reactive vaccination polict in outbreak prevention and control,” BMC Medicine, vol. 13, p. 271, 2015.

H. Feldmann and T. W. Geisbert, “Ebola haemorrhagic fever,” Lancet, vol. 377, no. 9768, pp. 849–862, 2011.

P. Francesconi, Z. Yoti, S. Declich, P. A. Onek, M. Fabiani, J. Olango, R. Andraghetti, P. E. Rollin, C. Opira, D. Greco, and S. Salmaso, “Ebola hemorrhagic fever transmission and risk factors of contacts, Uganda,” Emerging Infectious Diseases, vol. 9, no. 11, pp. 1430–1437, 2003.

S. V. Scarpino, A. Iamarino, C. Wells, D. Yamin, M. Ndeffo- Mbah, N. S. Wenzel, S. J. Fox, T. Nyenswah, F. L. Altice, A. P. Galvani et al., “Epidemiological and viral genomic se- quence analysis of the 2014 Ebola outbreak reveals clustered transmission,” Clinical Infectious Diseases, p. ciu1131, 2014.

S. F. Dowell, R. Mukunu, T. G. Ksiazek, A. S. Khan, P. E. Rollin, and C. Peters, “Transmission of Ebola hemorrhagic fever: a study of risk factors in family members, Kikwit, Democratic Republic of the Congo, 1995,” Journal of Infectious Diseases, vol. 179, no. Supplement 1, pp. S87–S91, 1999.

A. Matanock, M. A. Arwady, P. Ayscue, J. D. Forrester, B. Gaddis, J. C. Hunter, B. Monroe, S. K. Pillai, C. Reed, I. J. Schafer, M. Massaquoi, B. Dahn, and K. M. De Cock, “Ebola Virus Disease cases among health care workers not working in Ebola treatment units - Liberia, June-August, 2014,” Morbidity and Mortality Weekly Report, vol. 63, no. 46, pp. 1077–1081, 2014.

D. Yamin, S. Gertler, M. L. Ndeffo-Mbah, L. A. Skrip, M. Fal- lah, T. G. Nyenswah, F. L. Altice, and A. P. Galvani, “Effect of Ebola progression on transmission and control in Liberia,” Annals of Internal Medicine, vol. 162, no. 1, pp. 11–17, 2015.

J.Mossong,N.Hens,M.Jit,P.Beutels,K.Auranen,R.Mikola- jczyk, M. Massari, S. Salmaso, G. S. Tomba, J. Wallinga et al., “Social contacts and mixing patterns relevant to the spread of infectious diseases,” PLoS Med, vol. 5, no. 3, p. e74, 2008.

A. S. Khan, F. K. Tshioko, D. L. Heymann, B. Le Guenno, P. Nabeth, B. Kerstiens, Y. Fleerackers, P. H. Kilmarx, G. R. Rodier, O. Nkuku, P. E. Rollin, A. Sanchez, R. Swanepoel, O. Tomori, S. T. Nichol, C. J. Peters, J.-J. Muyembe-Tamfum, and T. G. Ksiazek, “The reemergence of Ebola hemorrhagic fever, Democratic Republic of Congo, 1995,” Journal of Infec- tious Diseases, vol. 179, no. S1, pp. S76–S86, 1999.

D.S.Chertow,C.Kleine,J.K.Edwards,R.Scaini,R.Giuliani, and A. Sprecher, “Ebola virus disease in West Africa—clinical manifestations and management,” New England Journal of Medicine, vol. 371, no. 22, pp. 2054–2057, 2014.

A. M. Henao-Restrepo, I. M. Longini, M. Egger, N. E. Dean, W. J. Edmunds, A. Camacho, M. W. Carroll, M. Doumbia, B. Draguez, S. Duraffour et al., “Efficacy and effectiveness of an rVSV-vectored vaccine expressing Ebola surface glycopro- tein: interim results from the Guinea ring vaccination cluster- randomised trial,” The Lancet, vol. 386, no. 9996, pp. 857–866, 2015.

G. Chowell, N. W. Hengartner, C. Castillo-Chavez, P. W. Fenimore, and J. Hyman, “The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda,” Journal of Theoretical Biology, vol. 229,

no. 1, pp. 119–126, 2004.

P. E. Lekone and B. F. Finkensta ̈dt, “Statistical inference in

a stochastic epidemic SEIR model with control intervention: Ebola as a case study,” Biometrics, vol. 62, no. 4, pp. 1170– 1177, 2006.

J. Legrand, R. Grais, P. Boelle, A. Valleron, and A. Flahault, “Understanding the dynamics of Ebola epidemics,” Epidemiol- ogy and Infection, vol. 135, no. 04, pp. 610–621, 2007.

J.M.Drake,I.Bakach,M.R.Just,S.M.O’Regan,M.Gambhir, and I. C.-H. Fung, “Transmission models of historical Ebola outbreaks,” Emerging Infectious Diseases, vol. 21, no. 8, p. 1447, 2015.

J. S. Weitz and J. Dushoff, “Modeling post-death transmission of Ebola: Challenges for inference and opportunities for con- trol,” Scientific Reports, vol. 5, 2015.

C. M. Rivers, E. T. Lofgren, M. Marathe, S. Eubank, and B. L. Lewis, “Modeling the impact of interventions on an epidemic of Ebola in Sierra Leone and Liberia,” PLoS Currents, vol. 6, 2014.

B. Tsanou, G. M. Moremedi, R. Kaondera-Shava, J. M. Lubuma, and N. Morris, “A simple mathematical model for Ebola in Africa,” Biomath Communications, vol. 2, no. 1, 2015.

L. Valdez, H. H. A. Reˆgo, H. Stanley, and L. Braunstein, “Predicting the extinction of Ebola spreading in Liberia due to mitigation strategies,” arXiv preprint arXiv:1502.01326, 2015.

A.Pandey,K.E.Atkins,J.Medlock,N.Wenzel,J.P.Townsend, J. E. Childs, T. G. Nyenswah, M. L. Ndeffo-Mbah, and A. P. Galvani, “Strategies for containing Ebola in West Africa,” Science, vol. 346, no. 6212, pp. 991–995, 2014.

M. F. Gomes, A. P. y Piontti, L. Rossi, D. Chao, I. Longini, M. E. Halloran, and A. Vespignani, “Assessing the international spreading risk associated with the 2014 West African Ebola outbreak,” PLoS Currents, vol. 6, 2014.

S.Merler,M.Ajelli,L.Fumanelli,M.F.Gomes,A.P.yPiontti, L. Rossi, D. L. Chao, I. M. Longini, M. E. Halloran, and A. Vespignani, “Spatiotemporal spread of the 2014 outbreak of Ebola virus disease in Liberia and the effectiveness of non-pharmaceutical interventions: a computational modelling analysis,” The Lancet Infectious Diseases, vol. 15, no. 2, pp. 204–211, 2015.

J. M. Drake, R. Kaul, L. W. Alexander, S. M. O’Regan, A. M. Kramer, J. T. Pulliam, M. J. Ferrari, and A. W. Park, “Ebola cases and health system demand in Liberia,” PLoS Biol, vol. 13, no. 1, p. e1002056, 2015.

C. Wells, D. Yamin, M. L. Ndeffo-Mbah, N. Wenzel, S. G. Gaffney, J. P. Townsend, L. A. Meyers, M. Fallah, T. G. Nyenswah, F. L. Altice, K. E. Atkins, and A. P. Galvani, “Harnessing case isolation and ring vaccination to control Ebola,” PLoS Neglected Tropical Diseases, 2015.

G.Webb,C.Browne,X.Huo,O.Seydi,M.Seydi,andP.Magal, “A model of the 2014 Ebola epidemic in West Africa with contact tracing,” PLoS Currents, vol. 7, 2014.

D.Fisman,E.Khoo,andA.Tuite,“Earlyepidemicdynamicsof the West African 2014 Ebola outbreak: estimates derived with a simple two-parameter model,” PLoS Currents, vol. 6, 2014.

D. Rand, “Correlation equations and pair approximations for spatial ecologies,” Advanced ecological theory: principles and applications, vol. 100, 1999.

T.Kratz,P.Roddy,A.T.Oloma,B.Jeffs,D.P.Ciruelo,O.dela Rosa, and M. Borchert, “Ebola Virus Disease outbreak in Isiro, Democratic Republic of the Congo, 2012: signs and symptoms,management and outcomes,” PLoS ONE, vol. 10, no. 6, p.e0129333, 2015.

M. G. Burch, K. A. Jacobsen, J. H. Tien, and G. A. Rempala,

“Network-based analysis of a small ebola outbreak,” Math

Biosci Eng., vol. 1, no. 14, pp. 67–77, 2017.

M. Newman, Networks: an introduction. Oxford University

Press, 2010.

J. C. Miller, A. C. Slim, and E. M. Volz, “Edge-based compartmental modelling for infectious disease spread,” Journal of The Royal Society Interface, vol. 9, no. 70, pp. 890–906, 2012. [Online]. Available: http://rsif.royalsocietypublishing.org/content/9/70/890

S. Chib and E. Greenberg, “Understanding the metroplis- hastings algorithm,” The American Statistician, vol. 49, no. 4, pp. 327–335, 1995.

A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari,

and D. B. Rubin, Bayesian data analysis. Raton, FL, 2014, vol. 2.

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Published

2019-10-15

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Original Articles