The Mathematics of Infectious Diseases

The Mathematics of Infectious Diseases

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...

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Veröffentlicht in:SIAM review 2000-12, Vol.42 (4), p.599-653
1. Verfasser: Hethcote, Herbert W.
Format: Artikel
Sprache:eng
Schlagworte:
Age groups
Analysis. Health state
Antibodies
Approximation theory
Biological and medical sciences
Disease
Disease models
Diseases
Epidemics
Epidemiology
Exact sciences and technology
General aspects
Immunization
Infections
Infectious diseases
Initial value problems
Integral equations
Mathematical analysis
Mathematical models
Mathematics
Measles
Medical sciences
Ordinary differential equations
Parameter estimation
Partial differential equations
Public health. Hygiene
Public health. Hygiene-occupational medicine
Sciences and techniques of general use
Survey and Review
Vaccination
Vaccines
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Beschreibung
Zusammenfassung: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.
ISSN:0036-1445
1095-7200
DOI:10.1137/S0036144500371907