Bovine Respiratory Disease (BRD) is a prevalent infectious disease of respiratory tract in cattle, presenting challenges in accurate diagnosis and forecasting due to the complex interactions of multiple risk factors. Common methods, including mathematical epidemiological models and data-driven approaches such as machine learning models, face limitations such as difficult parameter estimation or the need for data across all potential outcomes, which is challenging given the scarcity and noise in observing BRD processes. In response to these challenges, we introduce a novel approach known as the Bayesian Deep Mechanistic method. This method couples a data-driven model with a mathematical epidemiological model while accounting for uncertainties within the processes. By utilising 265 lung ultrasound videos as sensor data from 163 animals across 9 farms in France, we trained a Bayesian deep learning model to predict the infection status (infected or non-infected) of an entire batch of 12 animals, also providing associated confidence levels. These predictions, coupled with their confidence levels, were used to filter out highly uncertain diagnoses and diffuse uncertainties into the parameterisation of a mathematical epidemiological model to forecast the progression of infected animals. Our findings highlight that considering the confidence levels (or uncertainties) of predictions enhances both the diagnosis and forecasting of BRD. Uncertainty-aware diagnosis reduced errors to 32 %, outperforming traditional automatic diagnosis. Forecast relying on veterinarian diagnoses, considered the most confident, had a 23 % error, whilst forecast taking into account diagnosis uncertainties had a close 27.2 % error. Building upon uncertainty-awareness, our future research could explore integrating multiple types of sensor data, such as video surveillance, audio recordings, and environmental parameters, to provide a comprehensive evaluation of animal health, employing multi-modal methods for processing this diverse data.