Bulletin of Mathematical Biology

, Volume 75, Issue 7, pp 1031–1050

On the Exact Measure of Disease Spread in Stochastic Epidemic Models

Original Article

DOI: 10.1007/s11538-013-9836-3

Cite this article as:
Artalejo, J.R. & Lopez-Herrero, M.J. Bull Math Biol (2013) 75: 1031. doi:10.1007/s11538-013-9836-3


The basic reproduction number, R0, is probably the most important quantity in epidemiology. It is used to measure the transmission potential during the initial phase of an epidemic. In this paper, we are specifically concerned with the quantification of the spread of a disease modeled by a Markov chain. Due to the occurrence of repeated contacts taking place between a typical infective individual and other individuals already infected before, R0 overestimates the average number of secondary infections. We present two alternative measures, namely, the exact reproduction number, Re0, and the population transmission number, Rp, that overcome this difficulty and provide valuable insight. The applicability of Re0 and Rp to control of disease spread is also examined.


Disease spread Basic reproduction number Stochastic epidemic Vaccination coverage 

Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  1. 1.Department of Statistics and Operations Research, Faculty of MathematicsComplutense University of MadridMadridSpain
  2. 2.School of StatisticsComplutense University of MadridMadridSpain

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