Our review of the practical use of R0 has focused, largely, on literature from a 2 year period, 2003 and 2004. The number of papers included here—and our review was by no means exhaustive—testifies to the current relevance of this important concept.
The methods used to calculate R0
from incidence data vary. Model fitting using standard optimization techniques is often used to estimate parameters, which are then used to determine R0
by either the survival function or next generation methods. Estimating the initial growth rate, r0
, has also been widely used. For multiple classes of infectives (e.g. vector-borne disease), we find examples both where R0
is defined per generation, and examples where it is defined per infection cycle (see §2.2
). Owing to the usual limitations in using real data, we note that models typically used ‘in the field’ are simple, deterministic and non-structured (but see Ferguson et al. 1999
; Lloyd-Smith et al. 2003
; Matthews et al. 2003
; and Riley et al. 2003
for counter examples).
The basic reproductive ratio for emerging or endemic pathogens described above has been estimated for two main purposes. First, R0
is estimated in order to gauge the relative risk associated with a pathogen. These estimates are then used to compare the transmissibility of the disease to other well-known (and better understood) pathogens. Unfortunately, some time is needed to accrue sufficient incidence data for these estimates of R0
, and typically, R0
is only quantified after the epidemic has run its course, or is at least well established. The degree to which R0
for one emerging infectious agent might be predictive of future novel pathogens is questionable (Mills et al. 2004
). Furthermore, a numerical estimate of R0
for a specific disease does not, in and of itself, inform public health measures. These values are instead used to justify severe or costly control measures (e.g. FMD; Ferguson et al. 2001
; Matthews et al. 2003
), or less severe, more sustainable measures (e.g. malaria on Principe; Hagmann et al. 2003
Evaluating these control measures reveals the second, and more important, use of R0
in the recent literature. In most of the studies outlined above, R0
is evaluated both before and after a putative control measure is applied, with the aim of determining which measures, at what magnitudes and in what combinations, are able to reduce R0
to a value less than one. The results of these efforts have clearly offered useful practical guidelines: in some cases the results are counter-intuitive (e.g. West Nile virus: Wonham et al. 2004
), in many cases they are sobering.
offers a simple, universal measure of control efficacy, it is important to note that using R0
for this purpose ignores other important issues, such as the timing of secondary infections, or the negative impact of control measures on the population. For example, it is possible that some patterns of quarantine may be roughly equivalent in their effect on R0
, but may have different effects on the growth rate of the epidemic. Matthews et al. (2003)
discuss the trade-off between reducing R0
and culling as few animals as possible; Lipsitch et al. (2003)
discuss similar trade-offs between reducing R0
and burdening the population with excessive quarantine. These studies suggest that R0
may not always be the best overall measure of control efficacy. In contrast, the total mortality or morbidity, the total number of affected farms and other such measures may offer more practical indicators of control success, and can be balanced against the associated costs (e.g. Gravenor et al. 2004
). We argue that R0
may be somewhat overused in evaluating control measures, presumably because it is more readily calculated than these alternative indicators, and is widely recognized and understood.
For host–pathogen interactions, R0
stresses the role of the pathogen. An alternative, more host-centred characterization has been suggested by Bowers (2001)
. Nicknamed the basic depression ratio, D0
measures the degree to which the infected host population is depressed below its uninfected equilibrium level. Consideration of both R0
allows modelling of the complex trade-offs in the evolution of host–pathogen interactions.
When control is targeted at specific subgroups, R0
is not a good indicator of the required control effort, and the type-reproduction number, T
, has been suggested instead (Roberts & Heesterbeek 2003
; Heesterbeek & Roberts in press
). This quantity is equivalent to R0
in homogeneous populations, but in heterogeneous populations it singles out the control effort required to achieve eradication when control is targeted towards a particular host type (or subset of types), rather than the population as a whole, assuming the other types cannot sustain an epidemic by themselves. In many cases, T
is easier to formulate than R0
and both share the same threshold behaviour.