Abstract
Immunization with the Bacillus Calmette-Guérin \(\left(BCG \right)\) vaccine is currently used in many parts of the world as a means of preventing tuberculosis even though it remains a highly controversial method of preventing tuberculosis disease. We develop a deterministic mathematical model for the transmission dynamics of tuberculosis to monitor the effect of BCG vaccine, which may wane over time and which is not 100 % effective, on tuberculosis epidemiology. The analysis of the presented model has provided conditions to guarantee the eradication of the disease in terms of three major parameters incorporated into the model; the vaccination coverage level, the waning rate and the efficacy of the vaccine.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Castillo-Chavez, C.: Dynamical models of Tuberculosis and their applications. Mathematical biosciences and engineering 1, 361–404 (2004)
Castillo-Chavez, C., Feng, Z., Huang, W.: On the computation Ro and its role on global stability. In: Castillo-Chavez, C., Blower, S., van den Driesschie, Kirschner, D., Yakubu, A.A. (eds.) Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA Volumes in Mathematics and its Applications, vol. 125, pp. 229–250. Springer, Heidelberg (2002)
Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J.: On the definition and the computation of the basic reproductive ratio R 0 in models of infectious diseases in heterogeneous populations. J. Math. Biol. 28(4), 365–382 (1990)
National Office of Statistics, http://www.ons.dz
INSP: Relevé Epidémiologique Mensuel (REM), 2000 à 2006, http://www.insp.dz
Vynnycky, E., Fine, P.E.M.: The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of. Epidemiol. Infect. 119, 183–201 (1997)
World Health Organization (WHO), Global tuberculosis control: surveillance, planning, financing: WHO report 2008, WHO/HTM/TB/2008.393 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Selmane, S. (2010). Stability Analysis of an SVLI Epidemic Model. In: Taniar, D., Gervasi, O., Murgante, B., Pardede, E., Apduhan, B.O. (eds) Computational Science and Its Applications – ICCSA 2010. ICCSA 2010. Lecture Notes in Computer Science, vol 6019. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12189-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-12189-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12188-3
Online ISBN: 978-3-642-12189-0
eBook Packages: Computer ScienceComputer Science (R0)