- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 759801, 8 pages
Approximate Solution of Tuberculosis Disease Population Dynamics Model
1Institute for Groundwater Studies, University of the Free State, P.O. Box 9300, Bloemfontein, South Africa
2Department of Mathematics, Faculty of Art & Sciences, Celal Bayar University, Muradiye Campus, 45047 Manisa, Turkey
Received 22 March 2013; Accepted 2 June 2013
Academic Editor: R. K. Bera
Copyright © 2013 Abdon Atangana and Necdet Bildik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- V. Kumar, A. K. Abbas, N. Fausto, and R. N. Mitchell, Robbins Basic Pathology, Saunders Elsevier, 8th edition, 2007.
- A. Konstantinos, Testing For Tuberculosis, vol. 33, Australian Prescriber, 2010.
- K. G. Castro, “Global tuberculosis challenges,” Emerging Infectious Disease, vol. 4, no. 3, pp. 408–409, 1998.
- C. Dye, Z. Fengzengb, S. Scheele, et al., “Evaluating the impact of tuberculosis control number of deathsprevented by short-course chemotherapy in China,” International Journal of Epidemiology, vol. 29, no. 3, pp. 558–564, 2000.
- L. Gammaitoni and M. C. Nucci, “Using a mathematical model to evaluate the efficacy of TB control measures,” Emerging Infectious Diseases, vol. 3, no. 3, pp. 335–342, 1997.
- C. J. Murray and J. A. Salomon, Using Mathematical Models To Evaluate Global Tuberculosis Control Strategies—A Paper Presented at the Centre For Population and Development Studies, Harvard University, Cambridge, Mass, USA, 1998.
- World health Organization, WHO: Tuberculosis Fact Sheet, 2007.
- O. K. Koriko and T. T. Yusuf, “Mathematical model to simulate tuberculosis disease population dynamics,” American Journal of Applied Sciences, vol. 5, no. 4, pp. 301–306, 2008.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods Series on Complexity, Nonlinearity and Chaos, World Scientific, 2012.
- A. Atangana, A. Ahmed, and N. Belic, “A generalized version of a low velocity impact between a rigid sphere and a transversely isotropic strain-hardening plate supported by a rigid substrate using the concept of non-integer derivatives,” Abstract Applied Analysis, vol. 2013, Article ID 671321, 9 pages, 2013.
- A. Atangana and J. F. Botha, “Analytical solution of the groundwater flow equation obtained via homotopy decomposition method,” Journal of Earth Science & Climatic Change, vol. 3, p. 115, 2012.
- A. Atangana and E. Alabaraoye, “Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor one-dimensional Keller-Segel equations,” Advances in Difference Equations, vol. 2013, p. 94, 2013.
- A. Atangana and A. Secer, “Time-fractional coupled- the korteweg-de vries equations,” Abstract Applied Analysis, vol. 2013, Article ID 947986, 8 pages, 2013.
- K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
- I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, 1999.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
- A. Atangana and A. Secer, “A note on fractional order derivatives and Table of fractional derivative of some specials functions,” Abstract Applied Analysis, vol. 2013, Article ID 279681, 2013.
- M. Caputo, “Linear models of dissipation whose Q is almost frequency independent, part II,” Geophysical Journal International, vol. 13, no. 5, pp. 529–539, 1967.
- S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus, Series on Complexity, Nonlinearity and Chaos, World Scientific, 2012, Models and numerical methods.
- A. Atangana and A. Kılıçman, “A possible generalization of acoustic wave equation using the concept of perturbed derivative order,” Mathematical Problems in Engineering, vol. 2013, Article ID 696597, 6 pages, 2013.