Uncertainty and sensitivity analysis of the basic reproductive rate: Tuberculosis as an example

Abstract

The basic reproductive rate (R(o)) is a measure of the severity of an epidemic. On the basis of replicated Latin hypercube sampling, the authors performed an uncertainty and sensitivity analysis of the basic reproductive rate of tuberculosis (TB). The uncertainty analysis allowed for the derivation of a frequency distribution for R(o) and the assessment of the relative contribution each of the three components of R(o) made when TB epidemics first arose centuries ago. (The three components of R(o) are associated with fast, slow, and relapse TB.) R(o) estimates indicated the existence of fairly severe epidemics when TB epidemics first arose. The R(o) for the susceptible persons who developed TB slowly (R(o)(slow) contributed the most to the R(o) estimates; however, the relative R(o)(slow) contribution decreased as the severity of TB epidemics increased. The sensitivity of the magnitude of R(o) to the uncertainty in estimating values of each of the input parameters was assessed. These results indicated that five of the nine input parameters' because of their estimation uncertainty, were influential in determining the magnitude of R(o). This uncertainty and sensitivity methodology provides results that can aid investigators in understanding the historical epidemiology of TB by quantifying the effect of the transmission processes involved. Additionally, this method can be applied to the R(o) of any other infectious disease to estimate the probability of an epidemic outbreak.