Inference in a metapopulation model of paratuberculosis in cattle via a composite-likelihood approximation
Résumé
Processes related to the spatio-temporal spread of pathogens in metapopulations are most often partially observed, especially for long-lasting endemic diseases. Bovine paratuberculosis (agent Mycobacterium avium subsp. paratuberculosis – Map) is a worldwide enzootic disease of economic importance for dairy cattle producers. Its screening in the field is difficult due to long incubation period and low sensitivity of routine diagnostic tests. Our objective was to estimate key parameters of a multiscale dynamical model of Map spread from longitudinal disease-related data to learn more about the infection dynamics of this disease.
Our approach is based on a mechanistic simulation model of Map spread between dairy herds, accounting for stochastic within-herd demography and infection dynamics, and animal trade between farms. Simulations were done at a regional scale and included a total of 12,857 dairy herds in Brittany (France), for which comprehensive data on cattle trade and partial data on animal infection status (2013 herds sampled from 2005 to 2013) were available.
Five key parameters of this model are: the proportion of initially infected herds, the within-herd initial prevalence in infected herds, the probability of purchasing infected cattle from outside the metapopulation, the local indirect transmission rate, and the sensitivity of the diagnostic test.
Since a diversity of metrics could be envisioned to evaluate the distance between observations and simulations, we compared the behavior of many of these metrics in an exploratory numerical study based on a grid of parameter values associated with simulated data sets. The most promising performances were obtained with metric built as a Monte-Carlo approximation of a composite likelihood accounting for correlation between consecutive sampling points. Inference was then conducted by coupling this composite likelihood approximation with a numerical optimization algorithm (Nelder-Mead)
After validation of the inference algorithm on simulated data sets, we estimated previously unknown key parameters of the model thereby providing new insights on Map spread at regional scale.