Total views : 314

Queueing Technique for Ebola Virus Disease Transmission and Control Analysis

Affiliations

  • Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia,81310 UTM Johor Bahru, Malaysia
  • UTM Centre for Industrial and Applied Mathematics, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
  • Department of Statistics & Operations Research, Modibbo Adama University of Technology, P.M.B 2076, Yola, Adamawa State, Nigeria

Abstract


Objective: The outbreak of Ebola Virus Disease (EVD) in different countries, especially the West African nations has been ravaging human lives and the economy. The ugly situation calls for urgent provision of sound EVD control measures. Methods/ Statistical Analysis: This paper proposes the queueing technique as a promising and efficient mathematical approach for the study of EVD transmission and control. It highlights the queueing theory governing equation and applies the theory to EVD problem. Findings: The application of the technique to the Guinea 2014 EVD outbreak indicates that the use of two quarantine centres to combat the outbreak would have served as an adequate control measure. This technique can be used to manage the manpower and material resources in the combat against EVD outbreak. Applications/Improvements: This approach brings to fore the possible use of queueing technique in the analysis of EVD outbreak. Transmission and control in other countries ravaged by EVD could be studied using queueing network models.

Keywords

Control Measure, Ebola, Epidemics, Queueing Technique, Transmission.

Full Text:

 |  (PDF views: 220)

References


  • Feldmann H, Geisbert TW. Ebolahaemorrhagic fever. Lancet. 2011; 377:849–62.
  • Lahm SA, Kombila M, Swanepoel R, Barnes RF. Morbidity and mortality of wild animals in relation to outbreaks of ebola haemorrhagic fever in Gabon, 1994 and 2003. Transactions of the Royal Society of Tropical Medicine and Hygiene. 2007; 101. p. 64–78.
  • Pigott DM, Golding N, Mylne A, Huang Z, Henry AJ., Weiss DJ, Brandy OJ, Kraemer MUG, Smith DL, Moyes CL, Bhatt S, Gething, PW, Horby PW, Bogoch II, Brownstein JS, Mekaru SR, Tatem AJ, Khan K, Hay SI. Mapping the zoonotic niche of ebola virus disease in Africa. Elife. 2014 Sep 8.
  • Walsh PD, Abernethy KA, Bermejo M, De Beyers R, Wachter P, Akou ME, Huijbregts B, Mambounga D.I., Toham A.K., Kilbourn AM, Lahm SA., Latour S, Maisels F, Mbina C, Mihindou Y, Obiang SN, Effa EN, Starkey MP, Telfer P, Thibault M, Tutin CE, White LJ, Wilkie DS. Catastrophic ape decline in western equatorial Africa. Nature. 2003; 422. p. 611–614.
  • Weber DJ, Fischer WA, Wohl DA, Rutala WA. Protecting healthcare personnel from acquiring Ebola virus disease. Infection control and hospital epidemiology. 2015; 36(10).
  • Wong JI, Zhang W, Kargbo D, Haque U, Hu W, Wu P, Kamara A, Chen Y, Kargbo B, Glass GE, Yang R, Cowling BJ, Liu C. Assessment of the severity of ebola virus disease in Sierra Leone 2014-2015. Epidemiol. Infect. 2015; 1–9. Cambridge University Press.
  • Geisbert TW. Microscopy in the hot zone: from the discovery of Ebola virus to a possible treatment. Microsc Microanal. 2004; 10(Suppl 2).
  • Jaime A, Delmar B, Milton G, Josue M, Francisco R, Noe V. Mathematical models to study the outbreaks of Ebola. 1996; https://dspace.library.com. Date accessed: 20/10/2014.
  • Chowell G, Hengartner NW, Castillo-Chavez C, Fenimore PW, Hyman JM. The basic reproduction number of Ebola and the effects of public health measures: the cases of Congo and Uganda. Journal of Theoretical Biology. 2004; 229. p. 119–126.
  • Khan AS, Tshioko K, Heymann DL, Guenno BL, Nabeth P, Kerstiens B, Fleerackers Y, Kilmarx PH, Rodier GR, Nkuku O, Rollin PE, Sanchez A, Zaki SR, Swanepoel R, Tomori O, Nichol ST, Peters CJ, Muyembe-Tamfum JJ, Ksiazek TG. The reemergence of Ebola Haemorrhagic Fever, Democratic Republic of the Congo, 1995. The Journal of Infectious Disease. 1999; 179. p. S76–S86.
  • World Health Organization. Outbreak of Ebola hemorrhagic fever, Uganda, August 2000-January 2001. Weekly Epidemiol, Record. 2001; 76. p. 41–48.
  • Lekone PE, Finkenstadt BF. Statistical inference in a stochastic epidemic SEIR models with control intervention: Ebola as a case study. Biometrics. PubMed PMID: 17156292. 2006 December. 62(4). p. 1170–7.
  • Gibson GJ, Renshaw E. Estimating parameters in stochastic compartmental models using Markov chain methods. IMA Journal of Mathematics in Applied Medicine and Biology. 1998; 15. p. 19–40.
  • Legrand J, Grais RF, Boelle PY, Valleron AJ, Flahault A. Understanding the dynamics of Ebola epidemics. Epidemiol Infect. PubMed PMID:16999875. 2007 May; 135(4). p.610–21.
  • Driessche VP, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences. 2002; 180. p. 29–48.
  • Isberg E. Are differential equations the proper tool to describe reality? http://www.researchgate.net. Date accessed: 19/05/2015.
  • Kendall D. Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. The Annals of Mathematical Statistics. 1953; 24. p. 338–354.
  • Kitaev M. The M/G/1 processor-sharing models: Transient behaviour. Queueing Systems. 1993; 14. p. 239–273.
  • Ball F, Donnelly P. Strong approximations for epidemic models. Stochastic Processes and their Applications. 1995; 55. p. 1–21.
  • Trapman P, Bootsma MCJ. A useful relationship between epidemiology and queueing theory: The distribution of the number of infectives at the moment of the first detection. Elsevier. Mathematical Biosciences. 2009; 219. p.15–22.
  • Hernandez-Suarez CM, Castillo-Chavez C, Montesinos LO, Hernandez-Cuevas K. An application of queuing theory to SIS and SEIS epidemic models. Mathematical Biosciences and Engineering. 2010; 7(4). p.809–823.
  • Okoro OJ. On Markovian Queueing Model as Birth-Death Process. Global Journal of Science Frontier Research Mathematics and Decision Sciences. 2013; 13(11):22–38.
  • Sztrik J. Basic queueing theory. University of Debrecen, Faculty of Informatics, http://irh.inf.unideb.hu/user/jsztrik; 2012. Date accessed: 20/10/ 2014.
  • Cooper RB. Introduction to queueing theory. Second Edition. Computer Systems and Management Science Florida. Florida Atlantic University. Boca Raton, Florida. Elsevier North Holland, Inc. New York: Oxford, 1981.
  • Winston WL. Operations research applications and algorithms. Fourth Edition. www.math.washington.edu/~billey/class/480/course.notes/. Winston.OperationsResearch.pdf; 2004. Date accessed 20/10/2014.
  • Bolch G, Greiner S, De Meer H, Trivedi KS. Queueing networks and Markov chains. John Wiley, 2nd edition.2006.
  • World Health Organisation. Database statistics (2015).http://apps.who.int/iris/bitstream/10665/170250/1/9789240694439_eng.pdf?ua=1. Date accessed 12/05/2015.

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.