Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Age-of-infection and the final size relation

1. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2

We establish the final size equation for a general age-of-infection epidemic model in a new simpler form if there are no disease deaths (total population size remains constant). If there are disease deaths, the final size relation is an inequality but we obtain an estimate for the final epidemic size.
  Figure/Table
  Supplementary
  Article Metrics

Keywords final size relation; epidemic models; basic reproduction number; age of infection

Citation: Fred Brauer. Age-of-infection and the final size relation. Mathematical Biosciences and Engineering, 2008, 5(4): 681-690. doi: 10.3934/mbe.2008.5.681

 

This article has been cited by

  • 1. Menachem Lachiany, Yoram Louzoun, Effects of distribution of infection rate on epidemic models, Physical Review E, 2016, 94, 2, 10.1103/PhysRevE.94.022409
  • 2. Nancy Hernandez-Ceron, Zhilan Feng, Carlos Castillo-Chavez, Discrete Epidemic Models with Arbitrary Stage Distributions and Applications to Disease Control, Bulletin of Mathematical Biology, 2013, 75, 10, 1716, 10.1007/s11538-013-9866-x
  • 3. Ashleigh Tuite, Beate Sander, Nick Pizzi, S.M. Moghadas, Amy Greer, S. Driedger, Fred Brauer, Chris Bauch, Julien Arino, P. van den Driessche, James Watmough, Jianhong Wu, Ping Yan, Pandemic influenza: Modelling and public health perspectives, Mathematical Biosciences and Engineering, 2011, 8, 1, 1, 10.3934/mbe.2011.8.1
  • 4. G. Katriel, R. Yaari, A. Huppert, U. Roll, L. Stone, Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study, Journal of The Royal Society Interface, 2011, 8, 59, 856, 10.1098/rsif.2010.0515
  • 5. Guy Katriel, The size of epidemics in populations with heterogeneous susceptibility, Journal of Mathematical Biology, 2012, 65, 2, 237, 10.1007/s00285-011-0460-2
  • 6. Fan Bai, Uniqueness of Nash equilibrium in vaccination games, Journal of Biological Dynamics, 2016, 10, 1, 395, 10.1080/17513758.2016.1213319
  • 7. Joel C. Miller, A Note on the Derivation of Epidemic Final Sizes, Bulletin of Mathematical Biology, 2012, 74, 9, 2125, 10.1007/s11538-012-9749-6
  • 8. Baltazar Espinoza, Victor Moreno, Derdei Bichara, Carlos Castillo-Chavez, , Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, 2016, Chapter 9, 123, 10.1007/978-3-319-40413-4_9
  • 9. Jummy Funke David, Epidemic models with heterogeneous mixing and indirect transmission, Journal of Biological Dynamics, 2018, 12, 1, 375, 10.1080/17513758.2018.1467506
  • 10. Fred Brauer, General compartmental epidemic models, Chinese Annals of Mathematics, Series B, 2010, 31, 3, 289, 10.1007/s11401-009-0454-1
  • 11. D. J. D. Earn, P. W. Andrews, B. M. Bolker, Population-level effects of suppressing fever, Proceedings of the Royal Society B: Biological Sciences, 2014, 281, 1778, 20132570, 10.1098/rspb.2013.2570
  • 12. Hiroshi Nishiura, Gerardo Chowell, Carlos Castillo-Chavez, Alessandro Vespignani, Did Modeling Overestimate the Transmission Potential of Pandemic (H1N1-2009)? Sample Size Estimation for Post-Epidemic Seroepidemiological Studies, PLoS ONE, 2011, 6, 3, e17908, 10.1371/journal.pone.0017908
  • 13. Fred Brauer, Mathematical epidemiology: Past, present, and future, Infectious Disease Modelling, 2017, 2, 2, 113, 10.1016/j.idm.2017.02.001
  • 14. Bahman Davoudi, Joel C. Miller, Rafael Meza, Lauren Ancel Meyers, David J. D. Earn, Babak Pourbohloul, Early Real-Time Estimation of the Basic Reproduction Number of Emerging Infectious Diseases, Physical Review X, 2012, 2, 3, 10.1103/PhysRevX.2.031005
  • 15. Ping Yan, Zhilan Feng, Variability order of the latent and the infectious periods in a deterministic SEIR epidemic model and evaluation of control effectiveness, Mathematical Biosciences, 2010, 224, 1, 43, 10.1016/j.mbs.2009.12.007
  • 16. GUY KATRIEL, STOCHASTIC DISCRETE-TIME AGE-OF-INFECTION EPIDEMIC MODELS, International Journal of Biomathematics, 2013, 06, 01, 1250066, 10.1142/S1793524512500660
  • 17. Karyn L. Sutton, Danielle Robbins, H.Thomas Banks, Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations, Mathematical Biosciences and Engineering, 2013, 10, 5/6, 1301, 10.3934/mbe.2013.10.1301
  • 18. G. Röst, Z. Vizi, I. Z. Kiss,  Pairwise approximation for SIR -type network epidemics with non-Markovian recovery , Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2018, 474, 2210, 20170695, 10.1098/rspa.2017.0695
  • 19. P. van den Driessche, Zhisheng Shuai, Fred Brauer, Dynamics of an age-of-infection cholera model, Mathematical Biosciences and Engineering, 2013, 10, 5/6, 1335, 10.3934/mbe.2013.10.1335
  • 20. L.F. Mondolfo, , Aluminum Alloys, 1976, 385, 10.1016/B978-0-408-70932-3.50088-7
  • 21. L.F. Mondolfo, , Aluminum Alloys, 1976, 384, 10.1016/B978-0-408-70932-3.50087-5
  • 22. L.F. Mondolfo, , Aluminum Alloys, 1976, 335, 10.1016/B978-0-408-70932-3.50058-9
  • 23. L.F. Mondolfo, , Aluminum Alloys, 1976, 413, 10.1016/B978-0-408-70932-3.50098-X
  • 24. L.F. Mondolfo, , Aluminum Alloys, 1976, 380, 10.1016/B978-0-408-70932-3.50083-8
  • 25. Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng, , Mathematical Models in Epidemiology, 2019, Chapter 1, 3, 10.1007/978-1-4939-9828-9_1
  • 26. Fred Brauer, A simple model for behaviour change in epidemics, BMC Public Health, 2011, 11, S1, 10.1186/1471-2458-11-S1-S3
  • 27. Calistus N. Ngonghala, Enahoro Iboi, Steffen Eikenberry, Matthew Scotch, Chandini Raina MacIntyre, Matthew H. Bonds, Abba B. Gumel, Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus, Mathematical Biosciences, 2020, 108364, 10.1016/j.mbs.2020.108364

Reader Comments

your name: *   your email: *  

Copyright Info: 2008, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved