Determining Important Parameters in Ebola Epidemics
Keywords:
Ebola, Hopf bifurcation, Sensitivity indices, Basic reproductive number, Prevalence.Abstract
The dynamics of Ebola can best be understood using a mathematical model that determines its dynamics in the community. The model designed in this study explicitly incorporates the latency period, the different transmission compartments, and immigration and emigration effects. The steady states of the system are analysed for existence of equilibria and their stability investigated. From qualitative analysis of the model, it is established that a disease-free equilibrium exists and is stable when
References
Center for Disease Control and Prevention (CDC). Ebola Hemorrhagic Fever, 2003.
E.T.W.Bowen, G.S.Platt, G.Lioyd, A.Baskerville, W.J. Harris and E.C. Vella.
World Health Organisation (WHO).
B.Beer, R.Knuth and A.Bukreyev.
C.Bu
M.Leroy, B.Kumulungui, X.Pourrut, P.Rouquet, A.Hassanin, P.Yaba, A.Delicat and T.Paweska.
J.P.Gonzalez, X. Pourrut and E. Leroy.
A.T.Peterson, J.T.Bauer and J.N. Mills.
Center for Disease Control and Prevention (CDC). Questions and Answers about Ebola Hemorrhagic Fever, 2009.
M.Bray. (2003).
H.Leirs, J.N. Mills, J.W. Krebs, J.E.Childs, D.Akaibe and N.Woollen.
World Health Organisation (WHO). Ebola Hemorrhagic Fever: disease outbreaks, Oct. 2003.
T.Oyok, C.Odonga, E.Mulwani and J.Abur.
World Health Organisation. Available: http://www.who.int/csr/disease/ebola/en/index.html. [ Aug. 13, 2012].
G.L. Mandell and J.E.R. Bennett. Marburg and Ebola virus Hemorrhagic Fevers. Principles and Practice of Infectious Diseases. Philidelphia. Pa: Churchill Livingstone Elsevier, 2005, pp. 10
N.Sullivan, Z.Y.Yang and G.J.Nabel.
L.Borio, T.Inglesby, C.J.Peters, A.L.Schmaljohn, J.M.Huges, P.B.Jahrling, T.Ksiazek, and K.M. Johnson.
J.Legrand, R.F. Grais, P.Y. Boelle, A.J.Valleron, and A.Flahault.
O.Diekmann and J.A.P. Heesterbeek. Mathematical Epidemiology of Infectious Diseases. New York: John Wiley, 2000, pp. 15
O. Diekmann, J.Heesterbeek and J.Metz.
W.O. Kermack and A.G. Mckendrick.
L.S.Luboobi, J.Y.T. Mugisha, and J.Kasozi. Importance of Mathematical Modelling of Biological and Biomedical Processes. Kampala: African Society for Biomathematics Series, 2004, pp. 5
B.Nannyonga, D.J.T Sumpter, J.Y.T.Mugisha, and L.S.Luboobi.
F.Brauer and C.Castillo-Chavez. Mathematical Models in Population Biology and Epidemiology. New York: Springer, 2001, pp. 12
G.Chowel, N.W. Hengartner, C.Castillo-Chavez, P.W. Fenimore, and J.M. Hyman.
J.Astacio, D.Briere, M.Guillen, J.Martinez, F.Rodriguez and N.Valenzuela- Campos.
F.E. Lekone and B.F. Finkenstadt.
P.Stechlinski. A Study of Infectious Disease Models with Switching. Ontario, Canada: Waterloo,2009, pp. 21-29.
P.van den Driessche and J.Watmough.
S.H. Strogatz. Nonlinear Dynamics and Chaos with Applications to Physics , Biology, Chemistry and Engineering. Cambridge: Perseus Pub., 1994, pp. 44-92.
N.Chitnis, J.M.Hyman and J.M.Cushing.
Cary Institute of Ecosystem Studies. Likelihood Methods in Ecology., Spain: Granada, Apr. 2011, pp. 1-25.
P.Francesconi, Z.. Yoti, S. Declich, P.A. Onek, M. Fabiani, J. Olango, R. Andraghetti, P.E. Rollin, C.Opira, D.Greco. and S.Salmaso.
Uganda Bureau of Statistics. Migration and Tourism Report IV (2002-2006). Kampala, Uganda, Jan. 2008, pp.1-29.
M.Lamunu, J.J.Lutwama, J.Kamugisha, A.Opio, J.Nambooze, N.Ndayimirije and S.Okware.
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