Abstract and Applied Analysis

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

Raúl Peralta, Cruz Vargas-De-León, and Pedro Miramontes

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccine-age, and mortality induced by the disease into the SIR epidemic model. It is assumed that the period of immunity induced by vaccines varies depending on the vaccine-age. Using the direct Lyapunov method with Volterra-type Lyapunov function, we show the global asymptotic stability of the infection-free and endemic steady states.

Article information

Source
Abstr. Appl. Anal., Volume 2015 (2015), Article ID 341854, 8 pages.

Dates
First available in Project Euclid: 15 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1429103747

Digital Object Identifier
doi:10.1155/2015/341854

Mathematical Reviews number (MathSciNet)
MR3312745

Zentralblatt MATH identifier
07095571

Citation

Peralta, Raúl; Vargas-De-León, Cruz; Miramontes, Pedro. Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age. Abstr. Appl. Anal. 2015 (2015), Article ID 341854, 8 pages. doi:10.1155/2015/341854. https://projecteuclid.org/euclid.aaa/1429103747


Export citation

References

  • 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.
  • 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.
  • S. A. Plotkin, “Correlates of protection induced by vaccination,” Clinical and Vaccine Immunology, vol. 17, no. 7, pp. 1055–1065, 2010.
  • S. A. Plotkin, “Complex correlates of protection after vaccination,” Clinical Infectious Diseases, vol. 56, no. 10, pp. 1458–1465, 2013.
  • 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.
  • M. Prelog, “Differential approaches for vaccination from childhood to old age,” Gerontology, vol. 59, no. 3, pp. 230–239, 2013.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • C. C. McCluskey, “Delay versus age-of-infection–-global stability,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3046–3049, 2010.
  • 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.
  • 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.
  • 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.
  • 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. \endinput