Export file:


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


  • Citation Only
  • Citation and Abstract

Calculation of $R_0$ for age-of-infection models

1. Harvard Graduate School of Education, Harvard University, Cambridge, MA 02138
2. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2

We consider age-of-infection epidemic models to describe multiple- stage epidemic models, including treatment. We derive an expression for the basic reproduction number $R_0$ in terms of the distributions of periods of stay in the various compartments. We find that, in the model without treatment, $R_0$ depends only on the mean periods in compartments, and not on the form of the distributions. In treatment models, $R_0$ depends on the form of the dis- tributions of stay in infective compartments from which members are removed for treatment, but the dependence for treatment compartments is only on the mean stay in the compartments. The results give a considerable simplification in the calculation of the basic reproduction number.
  Article Metrics

Keywords basic reproduction number; epidemic models; age-of-infection models; treatment models.

Citation: Christine K. Yang, Fred Brauer. Calculation of $R_0$ for age-of-infection models. Mathematical Biosciences and Engineering, 2008, 5(3): 585-599. doi: 10.3934/mbe.2008.5.585


This article has been cited by

  • 1. Carlos Llensa, David Juher, Joan Saldaña, On the early epidemic dynamics for pairwise models, Journal of Theoretical Biology, 2014, 352, 71, 10.1016/j.jtbi.2014.02.037
  • 2. Fred Brauer, General compartmental epidemic models, Chinese Annals of Mathematics, Series B, 2010, 31, 3, 289, 10.1007/s11401-009-0454-1
  • 3. Brandy Rapatski, Juan Tolosa, Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment, Mathematical Biosciences and Engineering, 2014, 11, 3, 599, 10.3934/mbe.2014.11.599
  • 4. 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
  • 5. Zhipeng Qiu, Zhilan Feng, Transmission Dynamics of an Influenza Model with Age of Infection and Antiviral Treatment, Journal of Dynamics and Differential Equations, 2010, 22, 4, 823, 10.1007/s10884-010-9178-x
  • 6. 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
  • 7. Gerardo Chowell, Fred Brauer, , Mathematical and Statistical Estimation Approaches in Epidemiology, 2009, Chapter 1, 1, 10.1007/978-90-481-2313-1_1
  • 8. Fred Brauer, James Watmough, Age of infection epidemic models with heterogeneous mixing, Journal of Biological Dynamics, 2009, 3, 2-3, 324, 10.1080/17513750802415822

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