In recent years researchers have investigated a growing number of weighted heterogeneous networks, where connections are not merely binary entities, but are proportional to the intensity or capacity of the connections among the various elements. Different degree centrality measures have been proposed for this kind of networks. In this work we propose weighted degree and strength centrality measures (WDC and WSC). Using a reducing factor we correct classical centrality measures (CD) to account for tie weights distribution. The bigger the departure from equal weights distribution, the greater the reduction. These measures are applied to a real network of Italian livestock movements as an example. A simulation model has been developed to predict disease spread into Italian regions according to animal movements and animal population density. Model's results, expressed as infected regions and number of times a region gets infected, were related to weighted and classical degree centrality measures. WDC and WSC were shown to be more efficient in predicting node's risk and vulnerability. The proposed measures and their application in an animal network could be used to support surveillance and infection control strategy plans.