Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2015, Article ID 341854, 8 pages
http://dx.doi.org/10.1155/2015/341854
Research Article

Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age

1Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, Avenida Universidad, 3000 Circuito Exterior, S/N, 04510 Delegación Coyoacán, DF, Mexico
2Centro de Ciencias de la Complejidad (C3), Torre de Ingeniería, UNAM, Ciudad Universitaria, Avenida Universidad, 3000 Circuito Exterior, S/N, 04510 Delegación Coyoacán, DF, Mexico
3Unidad de Medicina Experimental, Hospital General de México, Dr Balmis No. 148., Colonia Doctores, 06726 México, DF, Mexico

Received 22 November 2014; Accepted 12 January 2015

Academic Editor: Yanni Xiao

Copyright © 2015 Raúl Peralta 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. E. Vidor, “Evaluation of the persistence of vaccine-induced protection with human vaccines,” Journal of Comparative Pathology, vol. 142, supplement 1, pp. S96–S101, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. M. Aregay, Z. Shkedy, G. Molenberghs, M.-P. David, and F. Tibaldi, “Model-based estimates of long-term persistence of induced HPV antibodies: a flexible subject-specific approach,” Journal of Biopharmaceutical Statistics, vol. 23, no. 6, pp. 1228–1248, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. S. A. Plotkin, “Correlates of protection induced by vaccination,” Clinical and Vaccine Immunology, vol. 17, no. 7, pp. 1055–1065, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. S. A. Plotkin, “Complex correlates of protection after vaccination,” Clinical Infectious Diseases, vol. 56, no. 10, pp. 1458–1465, 2013. View at Publisher · View at Google Scholar · View at Scopus
  5. S. S. Chaves, P. Gargiullo, J. X. Zhang et al., “Loss of vaccine-induced immunity to varicella over time,” The New England Journal of Medicine, vol. 356, no. 11, pp. 1121–1129, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Prelog, “Differential approaches for vaccination from childhood to old age,” Gerontology, vol. 59, no. 3, pp. 230–239, 2013. View at Publisher · View at Google Scholar · View at Scopus
  7. N. Wood and C.-A. Siegrist, “Neonatal immunization: where do we stand?” Current Opinion in Infectious Diseases, vol. 24, no. 3, pp. 190–195, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. X. Duan, S. Yuan, and X. Li, “Global stability of an SVIR model with age of vaccination,” Applied Mathematics and Computation, vol. 226, pp. 528–540, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. M. Iannelli, M. Martcheva, and X.-Z. Li, “Strain replacement in an epidemic model with super-infection and perfect vaccination,” Mathematical Biosciences, vol. 195, no. 1, pp. 23–46, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. X.-Z. Li, J. Wang, and M. Ghosh, “Stability and bifurcation of an SIVS epidemic model with treatment and age of vaccination,” Applied Mathematical Modelling, vol. 34, no. 2, pp. 437–450, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. P. Magal, C. C. McCluskey, and G. F. Webb, “Lyapunov functional and global asymptotic stability for an infection-age model,” Applicable Analysis, vol. 89, no. 7, pp. 1109–1140, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. C. C. McCluskey, “Delay versus age-of-infection—global stability,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3046–3049, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. A. V. Melnik and A. Korobeinikov, “Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility,” Mathematical Biosciences and Engineering, vol. 10, no. 2, pp. 369–378, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. C. Vargas-De-León, L. Esteva, and A. Korobeinikov, “Age-dependency in host-vector models: the global analysis,” Applied Mathematics and Computation, vol. 243, pp. 969–981, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  15. K. Mischaikow, H. Smith, and H. R. Thieme, “Asymptotically autonomous semiflows: chain recurrence and Lyapunov functions,” Transactions of the American Mathematical Society, vol. 347, no. 5, pp. 1669–1685, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  16. E. H. Elbasha, “Global stability of equilibria in a two-sex HPV vaccination model,” Bulletin of Mathematical Biology, vol. 70, no. 3, pp. 894–909, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus