As respiratory diseases continue to impact millions of individuals annually, mathematical models are frequently employed to characterize the seasonal dynamics of such outbreaks. However, these models often fall short in providing early detection of outbreak onset and peak, and are inherently affected by real-world sources of uncertainty. In this work, I first introduce an Early Warning System (EWS) designed to anticipate the onset and peak of respiratory outbreaks by aggregating diverse proxy signals, including Google search trends and Influenza Like Illness (ILI) data from neighboring regions. I propose extending this system through disease-specific transfer learning to enhance its adaptability across different respiratory illnesses. Second, I address the statistical challenge of uncertainty quantification in epidemic modeling by embedding SEIR (Susceptible-Exposed-Infected-Recovered) dynamics within a Bayesian inference framework. Using synthetic data and controlled experimental settings, I demonstrate how factors such as observational noise, data availability, and model complexity affect the posterior uncertainty and reliability of parameter estimates. As a next step, I propose applying this inference pipeline to real-world epidemiological data to evaluate its performance under more realistic conditions. Finally, I outline future research directions involving the application of neural networks to other complex domains, such as modeling black hole dynamics or using retinal imaging data for early cancer detection.