On the Exact Measure of Disease Spread in Stochastic Epidemic Models

The basic reproduction number, R 0 , 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...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2013-07, Vol.75 (7), p.1031-1050
Main Authors: Artalejo, J. R., Lopez-Herrero, M. J.
Format: Article
Language:English
Subjects:
Cell Biology
Communicable Diseases - epidemiology
Communicable Diseases - transmission
Disease spread
Epidemics - statistics & numerical data
Humans
Infection Control - methods
Infection Control - statistics & numerical data
Life Sciences
Markov Chains
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Models, Biological
Models, Statistical
Original Article
Stochastic Processes
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Summary:The basic reproduction number, R 0 , 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, R 0 overestimates the average number of secondary infections. We present two alternative measures, namely, the exact reproduction number, R e 0 , and the population transmission number, R p , that overcome this difficulty and provide valuable insight. The applicability of R e 0 and R p to control of disease spread is also examined.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-013-9836-3