Growth rates in epidemic models: application to a model for HIV/AIDS progression.

The most common quantity used to describe the growth of an epidemic when modelling infectious diseases is the basic reproduction number R0. While R0 is most appropriate for epidemics with short-lasting infections, long-lasting infections such as HIV/AIDS may call for the use of growth rates with other properties. For a group of multi-state compartment models we define both R0, the actual reproduction number Ra(t), and the intrinsic growth rate r. We study the relationship between these different reproduction numbers and growth rates and take a brief look at how they could be estimated from actual observed data. The work is illustrated by a model for HIV/AIDS progression among homosexual men in England and Wales. We conclude that other measures of growth, in addition to R0, give important supplementary information.