Skip to main content
SpringerLink
Log in

Introduction to Compartmental Models in Epidemiology

  • Conference paper
  • First Online:
Mathematical Analysis for Transmission of COVID-19

Part of the book series: Mathematical Engineering ((MATHENGIN))

  • 572 Accesses

Abstract

In this chapter, we discuss the basics of compartmental models in epidemiology and requisite analysis.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Similar content being viewed by others

References

  1. Allen, L., & Bridges, T. J. (2002). Numerical exterior algebra and the compound matrix method. Numerische Mathematik, 92(2), 197–232.

    Article  MathSciNet  Google Scholar 

  2. Awan, A. U., & Sharif, A. (2017). Smoking model with cravings to smoke. Advanced Studies in Biology, 9(1), 31–41.

    Article  Google Scholar 

  3. Busenberg, S., & Van den Driessche, P. (1990). Analysis of a disease transmission model in a population with varying size. Journal of Mathematical Biology, 28(3), 257–270.

    Google Scholar 

  4. Cai, L., Li, X., Ghosh, M., & Guo, B. (2009). Stability analysis of an HIV/AIDS epidemic model with treatment. Journal of Computational and Applied Mathematics, 229(1), 313–323.

    Article  MathSciNet  Google Scholar 

  5. Diekmann, O., Heesterback, J. A. P., & Roberts, M. G. (2009). The construction of next generation matrices for compartmental epidemic models. Journal of the Royal Society Interface, 7(47), 873–885.

    Article  Google Scholar 

  6. Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28(4), 365–382.

    Article  MathSciNet  Google Scholar 

  7. Dublin, L. I., & Lotka, A. J. (1925). On the true rate of natural increase: As exemplified by the population of the United States, 1920. Journal of the American Statistical Association, 20(151), 305–339.

    Google Scholar 

  8. Fleming, W. H., & Rishel, R. W. (2012). Deterministic and stochastic optimal control (Vol. 1). Berlin: Springer Science & Business Media.

    Google Scholar 

  9. Guo, H., Li, M. Y., & Shuai, Z. (2008). A graph-theoretic approach to the method of global Lyapunov functions. Proceedings of the American Mathematical Society, 136(8), 2793–2802.

    Article  MathSciNet  Google Scholar 

  10. Johnson, L. (2004). An introduction to the mathematics of HIV/AIDS modelling. Centre for Actuarial Research. https://pdfs.semanticscholar.org/7aef/2398872b9f791ab466ee034a633915d384ca.pdf.

  11. Kuczynski, R. R. (1931). The balance of births and deaths (Vol. 29). New York: Macmillan.

    Google Scholar 

  12. LaSalle, J. P. (1976). The stability of dynamical systems. Philadelphia, PA: Society for Industrial and Applied Mathematics.

    Book  Google Scholar 

  13. Li, M. Y., & Muldowney, J. S. (1996). A geometric approach to global-stability problems. SIAM Journal on Mathematical Analysis, 27(4), 1070–1083.

    Article  MathSciNet  Google Scholar 

  14. Li, Y., & Muldowney, J. S. (1993). On Bendixson’s criterion. Journal of Differential Equations, 106(1), 27–39.

    Article  MathSciNet  Google Scholar 

  15. Lotka, A. J. (1923). Contribution to the analysis of malaria epidemiology. II. General part (continued). Comparison of two formulae given by Sir Ronald Ross. American Journal of Hygiene, 3(Supp), 38–54.

    Google Scholar 

  16. Manika, D. (2013). Application of the compound matrix theory for the computation of Lyapunov exponents of autonomous Hamiltonian systems (Master’s thesis), Aristotle University of Thessaloniki.

    Google Scholar 

  17. Routh, E. J. (1877). A treatise on the stability of a given state of motion: Particularly steady motion. New York: Macmillan and Company.

    Google Scholar 

  18. Satia, M. H. (2020). Mathematical models for eco-friendly society (Ph.D. thesis). Gujarat University, Ahmedabad, India.

    Google Scholar 

  19. Smith, R. A. (1986). Some applications of Hausdorff dimension inequalities for ordinary differential equations. Proceedings of the Royal Society of Edinburgh Section a: Mathematics, 104(3–4), 235–259.

    Article  MathSciNet  Google Scholar 

  20. Van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1–2), 29–48.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Gujarat University, Ahmedabad, Gujarat, 380009, India

    Nita H. Shah

  2. Department of Mathematics, AIAS, Amity University Uttar Pradesh, Noida, Delhi, India

    Mandeep Mittal

Authors
  1. Nita H. Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mandeep Mittal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nita H. Shah .

Editor information

Editors and Affiliations

  1. Satellite Center, Ahmedabad, Gujarat, India

    Nita H. Shah

  2. Department of Mathematics, Amity Institute of Applied Sciences, Noida, Uttar Pradesh, India

    Mandeep Mittal

Rights and permissions

Reprints and permissions

Copyright information

© 2021 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

Shah, N.H., Mittal, M. (2021). Introduction to Compartmental Models in Epidemiology. In: Shah, N.H., Mittal, M. (eds) Mathematical Analysis for Transmission of COVID-19. Mathematical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-33-6264-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-981-33-6264-2_1

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-33-6263-5

  • Online ISBN: 978-981-33-6264-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation