Integration of Queueing Network into Susceptible Exposed Likely Infected Confirmed Dead Removed Model for Ebola Virus Disease Analysis

Ikeme John Dike^1, and Chinyere Ogochukwu Dike²

¹Department of Statistics & Operations Research, Modibbo Adama University of Technology, P.M.B 2076, Yola, Adamawa State, Nigeria

²Federal College of Education P.M.B 2042, Yola, Adamawa State, Nigeria

Cite this paper

Ikeme John Dike and Chinyere Ogochukwu Dike. Integration of Queueing Network into Susceptible Exposed Likely Infected Confirmed Dead Removed Model for Ebola Virus Disease Analysis. American Journal of Applied Mathematics and Statistics. 2018; 6(2):54-60. doi: 10.12691/AJAMS-6-2-3

Abstract

Ebola Virus Disease (EVD) is a complicated and unparalleled epidemic disease. In recent times, the disease has been ravaging human lives and economy in West African nations. The most affected countries are Guinea, Liberia and Sierra Leone. Contagious disease like Ebola transmits through networks, made by bodily interactions among persons. As a result of the transmission mode and deadly nature of the disease, this paper proposes an EVD transmission and control model which incorporates queueing network that considers all the transmission phases in order to understand the real nature of the disease and predict its behaviour. The result for network indicates that the population was vulnerable to large scale epidemics before intervention in the three countries. In network model, critical transmissibility or epidemic threshold is the least transmissibility necessary for an outbreak to turn into a large scale epidemic. The for the three countries was 0.0644. Before intervention, the transmissibility for Guinea was 0.1365, Liberia, 0.2093 and Sierra Leone, 0.1325. After intervention, the transmissibility for Guinea became 0.0595, Liberia, 0.0440 and Sierra Leone, 0.0571. The before and after transmissibility results in comparison with the indicate that intervention was effective in containing the EVD epidemic. The vulnerability decreased drastically after intervention.

Keywords

Ebola virus disease, epidemic, queueing network, transmission, control

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Baskett, F., Chandy, K.M., Muntz, R.R., Palacios, F.G.: Open, Closed and Mixed Networks of Queues with Different Classes of Customers. J. of the Asso. for Comput. Mach. 22(2), 249-260 (1975).
[2]	Central Intelligence Agency. CIA world factbook. https:www.cia.gov/library/publications/the-world-factbook/ (2016). Retrieved 2nd January 2017.
[3]	Chowell, G., Hengartner, N.W., Castillo-Chavez, C., Fenimore, P.W., Hyman, J.M.: The basic reproduction number of Ebola and the effects of public health measures: the cases of Congo and Uganda. J. of Theoret. Bio. 229(1), 119-26 (2004).
[4]	CHRD: Centre for Health Research and Diagnostics Guinea. www.dwu.ac.pg>index.php>centre (2015). Retrieved 2nd January 2017.
[5]	De Sterck, H., Miller, T., Manteuffel, T., Sanders, G.: Top-level acceleration of adaptive Algebraic Multilevel Methods for Steady-State Solution to Markov Chains. Advan. Comput. Math. 35, 375-403 (2011).
[6]	Dike, C.O., Zainuddin, Z.M., Ikeme John Dike, I.J.: Susceptible Infected Removed Epidemic Model Extension for Efficient Analysis of Ebola Virus Disease Transmission. American Scientific Publishers.
[7]	Gordon, W.J., Newell, G.F.: Closed queueing systems with exponential servers. Operations Research. 15(2), 254-265 (1967).
[8]	Guinea Age Structure: www.indexmundi.com/guinea/age_structure.html (2016). Retrieved 2nd January 2017.
[9]	Guinea Unemployment Rate: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=guinea+unemployment+rate (2017). Retrieved 2nd January 2017.
[10]	Hernandez-Suarez C.M., Castillo-Chavez C., Lopez O.M., and Hernandez-Cuevas K.: An application of queueing theory to SIS and SEIS epidemic models. Math. Biosci. and Eng. 7(4), 809-823 (2010).
[11]	International Religious Freedom Report: Liberia. United States Department of State, November 17, 2010. http://www.state.gov/g/drl/rls/irf/2010/148698.htm. Retrieved October 9, 2016.
[12]	Jackson, J.R.: Jobshop-like queueing systems, management science. 10(l), 131-142 (1963).
[13]	Kelly, F. P.: Networks of queues with customers of different types. J. of Appl. Probab. 12, 542-554 (1975).
[14]	Liberia Age Structure: www.indexmundi.com/liberia/age_structure.html (2016). Retrieved 2nd January 2017.
[15]	Liberia Unemployment Rate: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=liberia+unemployment+rate (2017). Retrieved 2nd January 2017.
[16]	Liu, Y.: Queueing networks as models of human performance and human-computer interaction. Proceedings of the 1994 Symposium on Human Interaction with Complex Systems. Department of Industrial and Operations Engineering, University of Michigan, USA. Technical Report 93-32. 1-15.
[17]	Meyers, L.A., Pourbohloul, B., Newman, M.E.J., Skowronski, D.M., Brunham, R.C.: Network theory and SARS: Predictng outbreak diversity. J. of Theoret. Bio. 232(1), 71-81 (2005).
[18]	MIDC: Establishment of Medical Imaging and Diagnostic Centre in Freetown. www.rvo.nl>projecten>establishment (2009). Retrieved 2nd January 2017.
[19]	Newman, M.E.J. (2002). The spread of epidemic disease on networks. Phys. Review E. 66, 016128.
[20]	NPHIL: National Public Health Institute of Liberia. www.ianphi.org>newprofiles>liberia (2014). Retrieved 2nd January 2017.
[21]	Ross, S.M. Introduction to probability models. (9th ed.). Academic Press, Elsevier Inc.: USA (2007)
[22]	Sierra Leone Age Structure: www.indexmundi.com/sierra_leone/age_structure.html (2016). Retrieved 2nd January 2017.
[23]	Sierra Leone Unemployment Rate: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=sierra+leone+unemployment+rate (2017). Retrieved 2nd January 2017.
[24]	Sztrik, J.: Basic Queueing Theory. http://irh.inf.unideb.hu/user/jsztrik (2012). Retrieved September, 2015.