Skip to main content

Variance of Infectious Periods and Reproduction Numbers for Network Epidemics with Non-Markovian Recovery

  • Conference paper
  • First Online:
  • 1072 Accesses

Part of the book series: Mathematics in Industry ((TECMI,volume 26))

Abstract

For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number when the mean infectious period is fixed.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

Learn about institutional subscriptions

References

  1. Carlos, L., Juher, D., Saldaña, J.: On the early epidemic dynamics for pairwise models. J. Theor. Biol. 352, 71–81 (2014)

    Article  MathSciNet  Google Scholar 

  2. Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J.: On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28(4), 365–382 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. Keeling, M.J.: The effects of local spatial structure on epidemiological invasions. Proc. R. Soc. Lond. B 266, 859–867 (1999)

    Article  Google Scholar 

  4. Kiss, I.Z., Röst, G., Vizi, Z.: Generalization of pairwise models to non-Markovian epidemics on networks. Phys. Rev. Lett. 115(7), 078701 (2015)

    Article  Google Scholar 

  5. Kiss, I.Z., Miller, J.C., Simon, L.P.: Mathematics of Epidemics on Networks – From Exact to Approximate Models. Springer, Berlin (2017)

    Book  MATH  Google Scholar 

  6. Knipl, D., Röst, G.: Large number of endemic equilibria for disease transmission models in patchy environment. Math. Biosci. 258, 201–222 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Nakata, Y., Röst, G.: Global analysis for spread of infectious diseases via transportation networks. J. Math. Biol. 70(6), 1411–1456 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Newman, M.E.J.: Spread of epidemic disease on networks. Phys. Rev. E 66(1), 016128 (2002)

    Article  MathSciNet  Google Scholar 

  9. Pastor-Satorras, R., Castellano, C., Van Mieghem, P., Vespignani, A.: Epidemic processes in complex networks. Rev. Mod. Phys. 87(3), 925 (2015)

    Article  MathSciNet  Google Scholar 

  10. Röst, G., Vizi, Z., Kiss, I.Z.: Impact of non-Markovian recovery on network epidemics. In: Mondaini, R.P. (ed.) BIOMAT 2015, pp. 40–53. World Scientific (2016)

    Google Scholar 

  11. Röst, G., Vizi, Z., Kiss, I.Z.: Pairwise approximation for SIR type network epidemics with non-Markovian recovery. arXiv:1605.02933 (2016)

    Google Scholar 

  12. Wilkinson, R.R., Ball, F.G., Sharkey, K.J.: The relationships between message passing, pairwise, Kermack-McKendrick and stochastic SIR epidemic models. arXiv:1605.03555 (2016)

    Google Scholar 

Download references

Acknowledgements

Research was supported by Hungarian Scientific Research Fund OTKA K109782

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gergely Röst .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Röst, G., Kiss, I.Z., Vizi, Z. (2017). Variance of Infectious Periods and Reproduction Numbers for Network Epidemics with Non-Markovian Recovery. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_25

Download citation

Publish with us

Policies and ethics