A precise definition of the basic reproduction number, R 0 , is presented for a general
compartmental disease transmission model based on a system of ordinary differential equations. It …

The basic reproduction number, R 0 is a measure of the potential for disease spread in a
population. Mathematically, R 0 is a threshold for stability of a disease-free equilibrium and is …

A final size relation is derived for a general class of epidemic models, including models with
multiple susceptible classes. The derivation depends on an explicit formula for the basic …

Severe acute respiratory syndrome (SARS), a new, highly contagious, viral disease, emerged
in China late in 2002 and quickly spread to 32 countries and regions causing in excess of …

It is shown that an SIS epidemic model with a non-constant contact rate may have multiple
stable equilibria, a backward bifurcation and hysteresis. The consequences for disease …

Stochastic simulations of network models have become the standard approach to studying
epidemics. We show that many of the predictions of these models can also be obtained from …

Determining sharp conditions for the global stability of equilibria remains one of the most
challenging problems in the analysis of models for the management and control of biological …

The phenomenon of backward bifurcation in disease models, where a stable endemic
equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction …

Compartmental models for influenza that include control by vaccination and antiviral
treatment are formulated. Analytic expressions for the basic reproduction number, control …

The control of severe acute respiratory syndrome (SARS), a fatal contagious viral disease
that spread to over 32 countries in 2003, was based on quarantine of latently infected …