Journal
SIAM REVIEW
Volume 42, Issue 4, Pages 599-653Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036144500371907
Keywords
thresholds; basic reproduction number; contact number; epidemiology; infectious diseases
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Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R-0, the contact number sigma, and the replacement number R are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for R-0 are obtained for MSEIR and SEIR endemic models with either continous age or age groups. Values of R-0 and sigma are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.
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