The Mathematics of Infectious Diseases
0036-1445
Abstract
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.