Skip to main content

Global Stability Analysis of HBV Epidemics with Vital Dynamics

  • Conference paper
  • First Online:
Proceedings of Sixth International Congress on Information and Communication Technology

Abstract

A mathematical model to predict the transmission process of Hepatitis B virus was developed. We established the existence and the positivity solution of the model. The model threshold quantity is defined and the analysis on global stability of the equilibrium is done using the known Lyapunov method and the comparison theorem method. Finally, computational simulation is presented to validate the analytical solution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. CDC (2020) Public Health Service inter-agency guidelines for screening donors of blood, plasma, organs, tissues, and semen for evidence of hepatitis B and hepatitis C, MMWR 40

    Google Scholar 

  2. Mann J, Roberts M (2011) Modelling the epidemiology of hepatitis B in New Zealand. J Theor Biol 269:266–272

    Article  MathSciNet  Google Scholar 

  3. Lavanchy D (2004) Hepatitis B virus epidemiology, disease burden, treatment, and current and emerging prevention and control measures. J Viral Hepat 11:97–107

    Article  Google Scholar 

  4. Lok AS, Heathcote EJ, Hoofnagle JH (2000) Management of hepatitis B,—Summary of a workshop. Gastroenterology 120:1828–1853

    Article  Google Scholar 

  5. Okuonghae D, Gumel AB, Sali MA (2015) Dynamics of a two strain vaccination model for polio. Nonlinear Anal Real World Appl 25:167–189

    Article  MathSciNet  Google Scholar 

  6. Chang MH (2007) Hepatitis virus infection Semin. Fetal Neonatal Med 12:160–167

    Article  Google Scholar 

  7. Wang J, Pang J, Liu X (2014) Modelling diseases with relapse and nonlinear incidence of infection: a multi-group epidemic model. J Biol Dyn 8:99–116

    Article  MathSciNet  Google Scholar 

  8. Zaman G, Kang YH, Jung IH (2008) Stability and optimal vaccination of an SIR epidemicmodel. BioSystems 93:240–249

    Article  Google Scholar 

  9. Zaman G, Kang YH, Jung IH (2009) Optimal treatment of an SIR epidemic model with time delay. BioSystems 98(2009):43–50

    Article  Google Scholar 

  10. WHO, see https://www.afro.who.int/health-topics/hepatitis. Accessed 3 Jan 2020

  11. Anderson RM, May RM (1991) Infectious disease of humans, dynamics and control. Oxford University Press, Oxford

    Google Scholar 

  12. Shepard CW, Simard EP, Finelli L, Fiore AE, Bell BP (2006) Hepatitis B virus infection epidemiology and vaccination. Epidemiol Rev 28:112–125

    Article  Google Scholar 

  13. Driessche P, Watmough J (2002) Reproduction number and subthreshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29–48

    Article  MathSciNet  Google Scholar 

  14. Thornley S, Bullen C, Roberts M (2008) Hepatitis B inahighprevalenceNewZealandpopulation: Amathematicalmodel applied to infection control policy. J Theor Biol 254:599–603

    Article  Google Scholar 

  15. LaSalle JP (1976) The stability of dynamical systems, regional conference series in applied mathematics. SIAM, Philadelphia, PA, USA

    Google Scholar 

  16. Kamuhanda AE, Shaibu O, Mary W (2018) Mathematical modelling and analysis of the dynamics of cholera. Global J Pure Appl Math 14(9)1259–1275

    Google Scholar 

  17. Khan T, Ahmad S, Zaman G (2019) Modeling and qualitative analysis of a hepatitis B epidemic model. Chaos 29(10). https://doi.org/10.1063/1.5111699

  18. McMahon BJ (2005) Epidemiology and natural history of hepatitis B. Semn Liver Dis 25:3–8

    Article  Google Scholar 

  19. Wang J, Zhang R, Kuniya T (2015) The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes. J Biol Dyn 9:73–101

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Oludoun Olajumoke .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Olajumoke, O., Olukayode, A., James, N., Oluwakemi, A., Babatunde, G., Benedicta, A. (2022). Global Stability Analysis of HBV Epidemics with Vital Dynamics. In: Yang, XS., Sherratt, S., Dey, N., Joshi, A. (eds) Proceedings of Sixth International Congress on Information and Communication Technology. Lecture Notes in Networks and Systems, vol 217. Springer, Singapore. https://doi.org/10.1007/978-981-16-2102-4_49

Download citation

Publish with us

Policies and ethics