Abstract and Applied Analysis

Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency

Rodrigue Yves M’pika Massoukou, Suares Clovis Oukouomi Noutchie, and Richard Guiem

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

Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number R 0 .

Article information

Source
Abstr. Appl. Anal., Volume 2018 (2018), Article ID 8479638, 21 pages.

Dates
Received: 9 April 2018
Revised: 26 June 2018
Accepted: 18 July 2018
First available in Project Euclid: 19 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1537322517

Digital Object Identifier
doi:10.1155/2018/8479638

Mathematical Reviews number (MathSciNet)
MR3847504

Zentralblatt MATH identifier
07029296

Citation

M’pika Massoukou, Rodrigue Yves; Oukouomi Noutchie, Suares Clovis; Guiem, Richard. Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency. Abstr. Appl. Anal. 2018 (2018), Article ID 8479638, 21 pages. doi:10.1155/2018/8479638. https://projecteuclid.org/euclid.aaa/1537322517


Export citation

References

  • J. Xu and Y. Zhou, “Global stability of a multi-group model with generalized nonlinear incidence and vaccination age,” Discrete and Continuous Dynamical Systems - Series B, vol. 21, no. 3, pp. 977–996, 2016.
  • R. Peralta, C. Vargas-De-León, and P. Miramontes, “Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age,” Abstract and Applied Analysis, vol. 2015, Article ID 341854, 8 pages, 2015.
  • 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.
  • 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.
  • 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.
  • S. M. Blower and A. R. McLean, “Prophylactic vaccines, risk behavior change, and the probability of eradicating HIV in San Francisco,” Science, vol. 265, no. 5177, pp. 1451–1454, 1994.
  • D. Ding and X. Ding, “Global stability of multi-group vaccination epidemic models with delays,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 1991–1997, 2011.
  • J. Q. Li, Y. L. Yang, and Y. C. Zhou, “Global stability of an epidemic model with latent stage and vaccination,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 2163–2173, 2011.
  • G. P. Sahu and J. Dhar, “Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 36, no. 3, pp. 908–923, 2012.
  • X. Song, Y. Jiang, and H. Wei, “Analysis of a saturation incidence SVEIRS epidemic model with pulse and two time delays,” Applied Mathematics and Computation, vol. 214, no. 2, pp. 381–390, 2009.
  • J. Wang, J. Lang, and Y. Chen, “Global threshold dynamics of an SVIR model with age-dependent infection and relapse,” Journal of Biological Dynamics, vol. 11, no. suppl. 2, pp. 427–454, 2017.
  • J. Wang, R. Zhang, and T. Kuniya, “The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes,” Journal of Biological Dynamics, vol. 9, no. 1, pp. 73–101, 2015.
  • Y. Xiao and S. Tang, “Dynamics of infection with nonlinear incidence in a simple vaccination model,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4154–4163, 2010.
  • Y. Yang, S. Tang, X. Ren, H. Zhao, and C. Guo, “Global stability and optimal control for a tuberculosis model with vaccination and treatment,” Discrete and Continuous Dynamical Systems - Series B, vol. 21, no. 3, pp. 1009–1022, 2016.
  • 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.
  • J. Wang, X. Dong, and H. Sun, “Analysis of an SVEIR model with age-dependence vaccination, latency and relapse,” Journal of Nonlinear Sciences and Applications. JNSA, vol. 10, no. 7, pp. 3755–3776, 2017.
  • M. Iannelli, Mathematical Theory of Age-Structured Population dynamics, Applied Mathematics Monographs, vol. 7, Consiglio Nazionale delle Ricerche, Giardini, Pisa, Italy, 1995.
  • G. F. Webb, Theory of Nonlinear Age-Dependent Population Dynamics, vol. 89, Marcel Dekker, New York, NY, USA, 1985.
  • H. L. Smith and H. R. Thieme, Dynamical systems and population persistence, vol. 118 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 2011.
  • J. Hale, Asymptotic Behavior of Dissipative System, vol. 25 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1988.
  • H. R. Thieme, “Uniform persistence and permanence for non-autonomous semiflows in population biology,” Mathematical Biosciences, vol. 166, no. 2, pp. 173–201, 2000.
  • P. Auger, R. Bravo de la Parra, J.-C. Poggiale, E. Sánchez, and T. Nguyen-Huu, “Aggregation of variables and applications to population dynamics,” in Structured Population Models in Biology and Epidemiology, P. Magal and S. Ruan, Eds., vol. 1936 of Lecture Notes in Mathematics, pp. 209–263, Springer, Berlin, Germany, 2008. \endinput