The Mathematics of Infectious Diseases
Herbert W. Hethcote
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Source: Crossref
Published: Jan 1, 2000
DOI: 10.1137/s0036144500371907
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Abstract. 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 [Formula: see text], the contact number [Formula: see text], and the replacement number [Formula: see text] are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for [Formula: see text] are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of [Formula: see text] and [Formula: see text] 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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