This paper presents Bayesian multivariate disease mapping and ecological regression models that take into account errors in covariates. Bayesian hierarchical formulations of multivariate disease models and covariate measurement models, with related methods of estimation and inference, are developed as an integral part of a Bayesian disability adjusted life years (DALYs) methodology for the analysis of multivariate disease or injury data and associated ecological risk factors and for small area DALYs estimation, inference, and mapping. The methodology facilitates the estimation of multivariate small area disease and injury rates and associated risk effects, evaluation of DALYs and 'preventable' DALYs, and identification of regions to which disease or injury prevention resources may be directed to reduce DALYs. The methodology interfaces and intersects the Bayesian disease mapping methodology and the global burden of disease framework such that the impact of disease, injury, and risk factors on population health may be evaluated to inform community health, health needs, and priority considerations for disease and injury prevention. A burden of injury study on road traffic accidents in local health areas in British Columbia, Canada, is presented as an illustrative example.