Assessing the risk of bluetongue to UK livestock: uncertainty and sensitivity analyses of a temperature-dependent model for the basic reproduction number

Abstract

Since 1998 bluetongue virus (BTV), which causes bluetongue, a non-contagious, insect-borne infectious disease of ruminants, has expanded northwards in Europe in an unprecedented series of incursions, suggesting that there is a risk to the large and valuable British livestock industry. The basic reproduction number, R(0), provides a powerful tool with which to assess the level of risk posed by a disease. In this paper, we compute R(0) for BTV in a population comprising two host species, cattle and sheep. Estimates for each parameter which influences R(0) were obtained from the published literature, using those applicable to the UK situation wherever possible. Moreover, explicit temperature dependence was included for those parameters for which it had been quantified. Uncertainty and sensitivity analyses based on Latin hypercube sampling and partial rank correlation coefficients identified temperature, the probability of transmission from host to vector and the vector to host ratio as being most important in determining the magnitude of R(0). The importance of temperature reflects the fact that it influences many processes involved in the transmission of BTV and, in particular, the biting rate, the extrinsic incubation period and the vector mortality rate.

Figure 1

Uncertainty analysis of the basic reproduction number for farms with (a,b) cattle only, (c,d) sheep only, or (e,f) both cattle and sheep. (a,c,e) Empirical CDFs for the basic reproduction number. The grey lines are the CDFs for individual replicates, while the black line is the CDF for all replicates combined. (b,d,f) Box and whisker plots showing R₀ and its dependence on temperature. The boxes show the lower quartile, median and upper quartile for R₀; the whiskers indicate 1.5 times the interquartile range; and the crosses indicate any outlying values. Results in each figure are based on 100 replicates of the LHS scheme.

Figure 2

Box and whisker plots of the PRCC between each parameter (see table 1 for definitions) and the basic reproduction number for farms with (a) cattle only, (b) sheep only, or (c) both cattle and sheep. The boxes show the lower quartile, median and upper quartile for the PRCC; the whiskers indicate 1.5 times the interquartile range; and the crosses indicate any outlying values. Results are based on 100 replicates of the LHS scheme.