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Afrika Matematika

, Volume 24, Issue 1, pp 55–68 | Cite as

Statistical data analysis of the 1995 Ebola outbreak in the Democratic Republic of Congo

  • D. NdanguzaEmail author
  • J. M. Tchuenche
  • H. Haario
Article

Abstract

Ebola is a lethal viral hemorrhagic fever with the potential to cause major epidemics. We analyse the 1995 outbreak in the Democratic Republic of Congo using two sets of data (onset and death data). Numerical simulations showed that the model fits the observed onset Ebola data at 99.95% and the observed death data at 98.6%. Since Bayesian inference cannot be performed analytically for complex models, Markov Chain Monte Carlo algorithm is then used as the second approach to obtain a solution. Results obtained from both approaches are contrasted and compared.

Keywords

Analysis Estimates Ebola Least squares Posterior distribution SEIR 

Mathematics Subject Classification (2000)

60J27 62-07 92D30 

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References

  1. 1.
    Bausch D.G., Sprecher A.G., Jeffs B., Boumandouki P.: Treatment of Marburg and Ebola hemorrhagic fevers: A strategy for testing new drugs and vaccines under outbreak conditions. Elsevier ScienceDirect 78, 150–161 (2008)Google Scholar
  2. 2.
    Bettencourt, L.M.A., Ribeiro, R.M.: Real Time Bayesian Estimation of the Epidemic Potential of Emerging Infectious Diseases. PLoS ONE 3(5), e2185 (2008). doi: 10.1371/journal.pone.0002185
  3. 3.
    Brauer, F., Wu, J., Van den Driessche, P.: Mathematical Epidemiology. Springer, Berlin, ISBN 978-3-540-78910-9 (2008)Google Scholar
  4. 4.
    Carr J.: Applications Centre Manifold theory. Springer, New York (1998)Google Scholar
  5. 5.
    Chowell G., Hengartner N.W., Castillo-Chavez C., Fenimore P.W., Hyman J.M.: The basic reproductive number of Ebola and the effects of public health measures: the case of Congo and Uganda. J. Theor. Biol. 229, 119–126 (2004)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Demiris, N.: Bayesian Inference for Stochastic Epidemic Models using Markov Chain Monte Carlo Methods, thesis for the degree of Doctor of Philosophy, Nottingham (2004)Google Scholar
  7. 7.
    Guardiola, J., Vecchio, A.: The basic reproduction number for infections dynamics models and the global stability of stationary points, Napoli, Italy (2003)Google Scholar
  8. 8.
    Haario H., Saksman E., Tamminen J.: An adaptive Metropolis algorithm. Bernouilli 7, 223–242 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Khan A.S., Tshioko K., Heymann D.L., LeGuenno B., Nabeth P., Kerstiens D.L., Fleerackers Y., Kilmarx P.H., Rodier G.R., Nkulu O., Rollin P.E., Sanchez A., Zaki S.R., Swanepoel R., Tomori O., Nichol S.T., Peters C.J., Muyembe-Tamfum J.J., Ksiazek T.G.: The re-emergence of Ebola hemorrhagic fever, Democratic Republic of the Congo, 1995. J. Infect. Dis. 179, 79–86 (1999)CrossRefGoogle Scholar
  10. 10.
    Kuhn, J.H.: Filoviruses: A compendium of 40 years of Epidemiologycal, Clinical, and Laboratory Studies, ISBN 978-3-211-20670-6 Springer, pp. 60–64 (2008)Google Scholar
  11. 11.
    Laine, M.: Adaptive MCMC Methods with Applications in Environmental and Geophysical Models, Ph.D. Thesis, Helsinki, ISBN 978-951-697-662-7 (2008)Google Scholar
  12. 12.
    Lekone P., Finkenstädt B.: Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 62, 1170–1177 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Leroy, EM., Rouquet, P., Formenty, P., Souquiere, S., Kilbourne, A., Froment, JM, Bermojo, M., Smit, S., Kareh, W., Swanepoel, R., Zaki, S.R., Rollin, P.E.: Multiple Ebola Virus transmission Events and Rapid Decline of Central African Wildlife, Science 303 (2004)Google Scholar
  14. 14.
    Morgan, B.J.T.: Applied Stochastic Modelling. Oxford University Press Inc., New York, ISBN 0340 74041 8 (2000)Google Scholar
  15. 15.
    Murray, J.D.: Mathematical Biology I: An introduction, 3rd edn. Springer, pp. 315–393 (2002)Google Scholar
  16. 16.
    Pourrut, X., Kumulungui, B., Wittmann, T. Moussavou, AD, Yaba, P., Nkoghe, D., Gonzalez, JP, Leroy, EM: The natural history of Ebola Virus in Africa. Microbes Infect 7, 1005–1014, Elsevier (2005)Google Scholar
  17. 17.
    Robert, P., Casella, G.: Monte Carlo Statistical Methods. Springer, New York, chapters 1-10, ISBN 0-387-21239-6 (2004)Google Scholar
  18. 18.
    Ryan, C.W. Hall, M.D., Richard, C.W. Hall, M.D., Marcia J. Chapman: The 1995 Kikwit Ebola outbreak: lessons hospitals and physicians can apply to future viral epidemics. J. Gen. Hosp. Psychiatry 30, 446–452, ScienceDirect, Elsevier (2008)Google Scholar
  19. 19.
    The World Health Organization (WHO). The world health report, 2007. (2007). Available at: http://www.who.int/whr/2007/whr07-en.pdf (accessed on November 2, 2008)
  20. 20.
    The World Health Organization Report. Ebola Outbreak Chronology (2004). Available at: http://www.who.int/mediacentre/factsheets/fs103/en/index1.html (accessed on November 4, 2008)

Copyright information

© African Mathematical Union and Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Applied MathematicsKigali Institute of Science and TechnologyKigaliRwanda
  2. 2.Mathematics DepartmentUniversity of Dar es SalaamDar es SalaamTanzania
  3. 3.Department of Mathematics and PhysicsLappeenranta University of TechnologyLappeenrantaFinland

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