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Herbert W. Hethcote

· University of Iowa

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Herbert W. Hethcote is a registered researcher in their academic field.

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Mathematical and Theoretical Epidemiology and Ecology Models, COVID-19 epidemiological studies, Evolution and Genetic Dynamics · 2000 · SIAM Review

The Mathematics of Infectious Diseases

Herbert W. Hethcote

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 R0, the contact number σ, and the replacement number R are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for R0 are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of R0 and σ 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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