Abstract
This chapter begins with introducing progressively more complex and realistic ODE models. It introduces the basic SEIR model, a model with an asymptomatic stage, a model with a carrier stage, a model with quarantine/isolation, a vaccination model, a tuberculosis model with treatment, and models with host and pathogen heterogeneities. The current state-of-the-art tools for the computation of the reproduction number in complex models, including the next-generation approach, are introduced and illustrated on examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C. Castillo-Chavez, Z. Feng, and W. Huang, On the computation of \(\mathcal{R}_{0}\) and its role on global stability, in Mathematical approaches for emerging and reemerging infectious diseases: an introduction (Minneapolis, MN, 1999), vol. 125 of IMA Vol. Math. Appl., Springer, New York, 2002, pp. 229–250.
O. Diekmann, J. A. P. Heesterbeek, and J. A. J. Metz, On thedefinition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), pp. 365–382.
Z. Feng, C. Castillo-Chavez, and A. Capurro, A model for tuberculosis with exogenous reinfection, Theor. Pop, Biol., 57 (2000), pp. 235–247.
Z. Feng and H. R. Thieme, Recurrent outbreaks of childhood diseases revisited: the impact of isolation, Math. Biosci., 128 (1995), pp. 93–130.
P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), pp. 29–48. John A. Jacquez memorial volume.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media New York
About this chapter
Cite this chapter
Martcheva, M. (2015). Techniques for Computing \(\mathcal{R}_{0}\) . In: An Introduction to Mathematical Epidemiology. Texts in Applied Mathematics, vol 61. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7612-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4899-7612-3_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-7611-6
Online ISBN: 978-1-4899-7612-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)