Volume 30 | Number 1 | Year 2016 | Article Id. IJMTT-V30P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V30P502
Most Mathematical model for Ebola virus in the literature had only the human population. This paper is an attempt to incorporate the host population which will give a clearer view of the transmission dynamics of the deadly disease. The disease free and endemic equilibrium of the model were obtained and analyzed for stability, . Key to our analysis is the basic reproductive number 0 R which is the number of secondary infections that one infective individual would create over the duration of the infectious period provided that everyone else is susceptible. We computed a numerical value for 0 R and conducted a sensitivity analysis of its parameters. Our results reveal that quarantine of infected individual’s speeds up recovery time.
[1] S. Baize , D. Pannetier, L. Oestereich, T. Rieger, L. Koivogui, N. Magassouba, B. Soropogui, M. S. Sow,S. Keïta, H. D. Clerck, A. Tiffany, G. Dominguez, M. Loua, A. Traoré, M. Kolié, E. R. Malano, E. Heleze, A. Bocquin, S. Mély, H. Raoul, V. Caro, D. Cadar, M. Gabriel, M. Pahlmann, D. Tappe, J. Schmidt-Chanasit, B. Impouma, A. K. Diallo, P. Formenty, M. Van Herp, ‘’Emergence of Zaire Ebola Virus Disease in Guinea - preliminary report’’.N Engl J Med, in press. 2014
[2] B. S. Hewlett, B. L. Hewlett, “ Ebola, Culture and Politics”: The Anthropology of an Emerging Disease. Cengage Learning. p. 103. 2007.
[3] J. W. King, (2008) "Ebola Virus". eMedicine. [Online]. Available: www.academia.edu/80740245/EBOLA
[4] (2014) The WHO "Ebola virus disease Fact sheet N°103" [Oline]. Available: www.who.int/mediacentre
[5] (2014) CDC Telebriefing on Ebola outbreak in West Africa". CDC. 2014-07-28. .
[6] B. Harden, (2001). "Dr. Matthew's Passion". New York Times Magazine. Retrieved 2008-02-25
[7] H. W. Hethcote, The mathematics of infectious diseases. SIAM Review. 42: 599-653. 2000.
[8] W. H. Hamer,. Epidemic Disease in England. Lancet 1: 733 – 739, 1960
[9] R. Rose, The Prevention of Malaria, 2nd ed., London: Murray, 1911.
[10] W. O. Kermack, and A. G. Mckendrick, A Contribution to Mathematical Theory of Epidemic, Raven, New York, 1927.
[11] A. Abdon, and F. D. G. Emile,(2014) “On the Mathematical Analysis of Ebola Hemorrhagic Fever: Deathly Infection Disease in West African Countries,” Hindawi Publishing Corporation, BioMed Research International,Volume 2014, 261383, 7 pages,
[12] Y. Zach, (2012) A Mathematical look at the EbolaVirus. [Online]. Available: http://www.home2.fvcc.edu/~dhicketh/DiffEqns/Spring2012P rojects/Zach%20Yarus%20- Final%20Project/Final%20Diffy%20Q%20project.pdf
[13] M. F. Gomes, A. P. 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 Outbreaks 2014.
[14] D. Fisman, E. Khoo, and A. Tuite, (2014). Early epidemic dynamics of the West African 2014 Ebola outbreak: estimates derived with a simple two-parameter model.PLOS Currents Outbreaks 2014
[15] C. L. Althaus, (2014) Estimating the reproduction number of Zaire ebolavirus (EBOV) during the 2014 outbreak in West Africa.PLOS Currents Outbreaks 2014
[16] H. W. Hethcote, “An Immunization Model for Heterogeneous Population,” Theoretical Population Biology,Vol 14, 338- 349, 1978.
[17] P. V. D. Driessche, and J. Wathmough, “Reproductive Number and Sub-Threshold Endemic Eqilibria for Compartment Modelling of Disease Transmission”. Mathematics BioscienceVol 180:29-48, 2005
[18] K. Dietz, “The Estimation of basic reproductive number R0 for infectious disease,” Statistical Methods in Medical Research, 2, 23-41.1993.
[19] M. G. Roberts, and J. A. P. Heesterbeek, “A new method for estimating the efforts require to control an infectious disease”, Preceeding of the Royal Society of London Series B, 270 pp. 1359-1364, 2003
[20] O. J. A. Diekmann, J. A. Heesterbeek, and J. A. J Metz. “On the definition and computation of basic reproductive ratio R0 in the model for infectious disease in a heterogeneous population”, Journal of Mathematical Biology, 28, 365-382 1990
[21] D. R. Powell, J. Faie, R. J. Leclaire, L. M. Moore, and D. Thompson, D. “Sensitivity Analysis of an Ifectious Disease Model”. International System Dynamic Conference,Boston, MA. 2005
Onuorah Martins .O., Nasir M.O., Ojo Moses S, Ademu, A, "A Deterministic Mathematical Model for Ebola Virus incorporating the Vector Population," International Journal of Mathematics Trends and Technology (IJMTT), vol. 30, no. 1, pp. 8-15, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V30P502