Improve Python GLM model fit for COVID Data

I'm seeking an expert in generalized linear modeling and machine learning to enhance my Python-based GLM Negative Binomial regression of COVID death counts. The current model shows severe misfit at high counts and non-normal residuals.

Key Requirements:
- Correct model specification
- Address over- and under-prediction
- Ensure well-behaved residuals

Ideal Skills and Experience:
- Proficiency in Python and GLM
- Strong background in machine learning
- Experience with regression analysis and residual diagnostics
- Ability to work with COVID-related datasets