Herbert W. Hethcote

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

Dynamical behavior of epidemiological models with nonlinear incidence rates

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Qualitative analyses of communicable disease models

, the contact number

Dynamics and control of the transmission of gonorrhea.

\sigma

Dynamic models of infectious diseases as regulators of population sizes

, and the replacement number

Epidemiological models with age structure, proportionate mixing, and cross-immunity.

R

Some epidemiological models with nonlinear incidence

are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for

Periodicity in Epidemiological Models

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Three Basic Epidemiological Models

are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of

An immunization model for a heterogeneous population

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