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2015, 12(5): 1055-1063. doi: 10.3934/mbe.2015.12.1055

Ebola outbreak in West Africa: real-time estimation and multiple-wave prediction

Xiang-Sheng Wang 1, and  Luoyi Zhong 1,

1. 

Department of Mathematics, Southeast Missouri State University, Cape Girardeau, MO 63701, United States, United States

Received  April 2015 Revised  May 2015 Published  June 2015

Based on the reported data until 18 March 2015 and numerical fitting via a simple formula of cumulative case number, we provide real-time estimation on basic reproduction number, inflection point, peak time and final outbreak size of ongoing Ebola outbreak in West Africa. From our simulation, we conclude that the first wave has passed its inflection point and predict that a second epidemic wave may appear in the near future.
Keywords: Ebola outbreak in West Africa, peak time., basic reproduction number, inflection point, final outbreak size.
Mathematics Subject Classification: Primary: 92B05; Secondary: 62P1.
Citation: Xiang-Sheng Wang, Luoyi Zhong. Ebola outbreak in West Africa: real-time estimation and multiple-wave prediction. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1055-1063. doi: 10.3934/mbe.2015.12.1055
References:
[1]

C. L. Althaus, Estimating the Reproduction Number of Ebola Virus (EBOV) During the 2014 Outbreak in West Africa, PLOS Currents Outbreaks, 2014. doi: 10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288.  Google Scholar

[2]

D. G. Bausch, J. S. Towner, S. F. Dowell, et al., Assessment of the risk of Ebola virus transmission from bodily fluids and fomites, The Journal of Infectious Diseases, 196 (2007), S142-147. doi: 10.1086/520545.  Google Scholar

[3]

Centers for Disease Control and Prevention, 2014 Ebola outbreak in West Africa - reported cases graphs, Available from: http://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/cumulative-cases-graphs.html. (Last accessed on 18 March 2015.) Google Scholar

[4]

Centers for Disease Control and Prevention, Ebola virus disease (EVD) information for clinicians in U.S. healthcare settings, Available from: http://www.cdc.gov/vhf/ebola/healthcare-us/preparing/clinicians.html. (Last accessed on 18 March 2015.) Google Scholar

[5]

G. Chowell, L. Simonsen, C. Viboud and Y. Kuang, Is West Africa approaching a catastrophic phase or is the 2014 Ebola epidemic slowing down? Different models yield different answers for Liberia, PLOS Currents Outbreaks, (2014), 1-12. doi: 10.1371/currents.outbreaks.b4690859d91684da963dc40e00f3da81.  Google Scholar

[6]

O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28 (1990), 365-382. doi: 10.1007/BF00178324.  Google Scholar

[7]

Y. H. Hsieh and Y. S. Cheng, Real-time forecast of multiphase outbreak, Emerging Infectious Diseases, 12 (2006), 122-127. doi: 10.3201/eid1201.050396.  Google Scholar

[8]

F. J. Richards, A flexible growth function for empirical use, Journal of Experimental Botany, 10 (1959), 290-301. doi: 10.1093/jxb/10.2.290.  Google Scholar

[9]

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[10]

X.-S. Wang, J. Wu and Y. Yang, Richards model revisited: Validation by and application to infection dynamics, Journal of Theoretical Biology, 313 (2012), 12-19. doi: 10.1016/j.jtbi.2012.07.024.  Google Scholar

[11]

World Health Organization, Ebola response roadmap situation report - 29 October 2014, Available from: http://apps.who.int/iris/bitstream/10665/137376/1/roadmapsitrep_29Oct2014_eng.pdf?ua=1. (Last accessed on 18 March 2015.) Google Scholar

[12]

World Health Organization, Situation reports with epidemiological data: Archive, Available from: http://apps.who.int/ebola/en/current-situation. (Last accessed on 18 March 2015.) Google Scholar

show all references

References:
[1]

C. L. Althaus, Estimating the Reproduction Number of Ebola Virus (EBOV) During the 2014 Outbreak in West Africa, PLOS Currents Outbreaks, 2014. doi: 10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288.  Google Scholar

[2]

D. G. Bausch, J. S. Towner, S. F. Dowell, et al., Assessment of the risk of Ebola virus transmission from bodily fluids and fomites, The Journal of Infectious Diseases, 196 (2007), S142-147. doi: 10.1086/520545.  Google Scholar

[3]

Centers for Disease Control and Prevention, 2014 Ebola outbreak in West Africa - reported cases graphs, Available from: http://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/cumulative-cases-graphs.html. (Last accessed on 18 March 2015.) Google Scholar

[4]

Centers for Disease Control and Prevention, Ebola virus disease (EVD) information for clinicians in U.S. healthcare settings, Available from: http://www.cdc.gov/vhf/ebola/healthcare-us/preparing/clinicians.html. (Last accessed on 18 March 2015.) Google Scholar

[5]

G. Chowell, L. Simonsen, C. Viboud and Y. Kuang, Is West Africa approaching a catastrophic phase or is the 2014 Ebola epidemic slowing down? Different models yield different answers for Liberia, PLOS Currents Outbreaks, (2014), 1-12. doi: 10.1371/currents.outbreaks.b4690859d91684da963dc40e00f3da81.  Google Scholar

[6]

O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28 (1990), 365-382. doi: 10.1007/BF00178324.  Google Scholar

[7]

Y. H. Hsieh and Y. S. Cheng, Real-time forecast of multiphase outbreak, Emerging Infectious Diseases, 12 (2006), 122-127. doi: 10.3201/eid1201.050396.  Google Scholar

[8]

F. J. Richards, A flexible growth function for empirical use, Journal of Experimental Botany, 10 (1959), 290-301. doi: 10.1093/jxb/10.2.290.  Google Scholar

[9]

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[10]

X.-S. Wang, J. Wu and Y. Yang, Richards model revisited: Validation by and application to infection dynamics, Journal of Theoretical Biology, 313 (2012), 12-19. doi: 10.1016/j.jtbi.2012.07.024.  Google Scholar

[11]

World Health Organization, Ebola response roadmap situation report - 29 October 2014, Available from: http://apps.who.int/iris/bitstream/10665/137376/1/roadmapsitrep_29Oct2014_eng.pdf?ua=1. (Last accessed on 18 March 2015.) Google Scholar

[12]

World Health Organization, Situation reports with epidemiological data: Archive, Available from: http://apps.who.int/ebola/en/current-situation. (Last accessed on 18 March 2015.) Google Scholar

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