Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 275902, 14 pages
http://dx.doi.org/10.1155/2012/275902
Research Article

Modeling the Dynamics of an Epidemic under Vaccination in Two Interacting Populations

Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa

Received 12 December 2011; Revised 11 April 2012; Accepted 18 April 2012

Academic Editor: Livija Cveticanin

Copyright © 2012 Ibrahim H. I. Ahmed et al. 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.

Linked References

  1. K. Chalvet-Monfray, M. Artzrouni, J. P. Gouteux, P. Auger, and P. Sabatier, “A two-patch model of Gambian sleeping sickness: Application to vector control strategies in a village and plantations,” Acta Biotheoretica, vol. 46, no. 3, pp. 207–222, 1998. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Tumwiine, J. Y. T. Mugisha, and L. S. Luboobi, “A host-vector model for malaria with infective immigrants,” Journal of Mathematical Analysis and Applications, vol. 361, no. 1, pp. 139–149, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. Y. Zhou, K. Khan, Z. Feng, and J. Wu, “Projection of tuberculosis incidence with increasing immigration trends,” Journal of Theoretical Biology, vol. 254, no. 2, pp. 215–228, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. Z. W. Jia, G. Y. Tang, Z. Jin et al., “Modeling the impact of immigration on the epidemiology of tuberculosis,” Theoretical Population Biology, vol. 73, no. 3, pp. 437–448, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. R. Naresh, A. Tripathi, and D. Sharma, “Modelling and analysis of the spread of AIDS epidemic with immigration of HIV infectives,” Mathematical and Computer Modelling, vol. 49, no. 5-6, pp. 880–892, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. M. De La Sen, R. P. Agarwal, A. Ibeas, and S. Alonso-Quesada, “On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination,” Informatica, vol. 22, no. 3, pp. 339–370, 2011. View at Google Scholar
  7. Y. Li, L. Chen, and K. Wang, “Permanence for a delayed nonautonomous SIR epidemic model with density-dependent birth rate,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 350892, 10 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. A. Kaddar, A. Abta, and H. T. Alaoui, “A comparison of delayed SIR and SEIR epidemic models,” Nonlinear Analysis: Modelling and Control, vol. 16, no. 2, pp. 181–190, 2011. View at Google Scholar · View at Scopus
  9. A. Lahrouz, L. Omari, and D. Kiouach, “Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model,” Nonlinear Analysis: Modelling and Control, vol. 16, no. 1, pp. 59–76, 2011. View at Google Scholar · View at Scopus
  10. G. Zaman, Y. Han Kang, and I. H. Jung, “Stability analysis and optimal vaccination of an SIR epidemic model,” BioSystems, vol. 93, no. 3, pp. 240–249, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. C. Piccolo III and L. Billings, “The effect of vaccinations in an immigrant model,” Mathematical and Computer Modelling, vol. 42, no. 3-4, pp. 291–299, 2005. View at Publisher · View at Google Scholar
  12. J. Yu, D. Jiang, and N. Shi, “Global stability of two-group SIR model with random perturbation,” Journal of Mathematical Analysis and Applications, vol. 360, no. 1, pp. 235–244, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. Z. Agur, L. Cojocaru, G. Mazor, R. M. Anderson, and Y. L. Danon, “Pulse mass measles vaccination across age cohorts,” Proceedings of the National Academy of Sciences of the United States of America, vol. 90, no. 24, pp. 11698–11702, 1993. View at Publisher · View at Google Scholar · View at Scopus
  14. L. Acedo, J.-A. Moraño, and J. Díez-Domingo, “Cost analysis of a vaccination strategy for respiratory syncytial virus (RSV) in a network model,” Mathematical and Computer Modelling, vol. 52, no. 7-8, pp. 1016–1022, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. J. M. Tchuenche, S. A. Khamis, F. B. Agusto, and S. C. Mpeshe, “Optimal control and sensitivity analysis of an influenza model with treatment and vaccination,” Acta Biotheoretica, vol. 59, no. 1, pp. 1–28, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models, Mathematical and Computational Biology Series, Chapman & Hall/CRC, London, UK, 2007.