Mathematical modeling of ovine footrot in the UK: the effect of Dichelobacter nodosus and Fusobacterium necrophorum on the disease dynamics

Dichelobacter nodosus is a virulent, invasive, anaerobic bacterium that is believed to be the causative agent of ovine footrot, an infectious bacterial disease of sheep that causes lameness. Another anaerobe, Fusobacterium necrophorum, has been intimately linked with the disease occurrence and severity. Here we examine data from a longitudinal study of footrot on one UK farm, including quantitative PCR (qPCR) estimates of bacterial load of D. nodosus and F. necrophorum. The data is at foot level; all feet were monitored for five weeks assessing disease severity (healthy, interdigital dermatitis (ID), or severe footrot (SFR)) and bacterial load (number of bacteria/swab). We investigate the role of D. nodosus and F. necrophorum in the progress of the disease using a continuous-time Markov model with 12 different states characterising the foot. The transition rates between the adjacent states are the (34) model parameters, these are determined using Metropolis Hasting MCMC. Our aim is to determine the predictive relationship between past and future D. nodosus and F. necrophorum load and disease states. We demonstrate a high level of predictive accuracy at the population level for the D. nodosus model, although the dynamics of individual feet is highly stochastic. However, we note that this predictive accuracy at population level is only high in more diseased states for F. necrophorum model. This supports our hypothesis that D. nodosus load and status of the foot work in combination to give rise to severe footrot and lameness, and that D. nodosus load plays the primary role in the initiation and progression of footrot, while F. necrophorum load rather increases disease severity of SFR.