Type 2 Diabetes (T2D) presents a challenge to healthcare systems and demands effective management to prevent serious health complications.

This PhD thesis presents algorithmic tools and models to improve T2D management. It presents a mathematical model for the glucose-insulin dynamics considering factors such as physical activity, stress, and different medications aiming to support treatment evaluation and medical education.

The work also proposes a stochastic model personalized with data from T2D individuals using particle Markov chain Monte Carlo methods.

Strategies to enhance glucose sensor readings are also developed and they show promising results over existing methods.

Additionally, the thesis proposes and evaluates different algorithms for long-acting insulin dosing, which demonstrate improved performance over current methods in virtual clinical trials.

Finally, the work investigates nudging strategies to promote medication adherence using an optimal control perspective, contributing to better T2D management outcomes.

The research provides a foundation for future tool development, aiming to benefit healthcare providers and improve the quality of life for individuals with T2D.