This research uses differential equations to model how people move between law-abiding life, crime, and incarceration. By simulating rehabilitation, overcrowding, and policy changes, the work shows how prisons can sometimes produce crime—and how evidence-based mathematical models can guide smarter decisions that reduce crime and build safer communities.

This research develops mathematical models to understand how honeybee clusters survive extreme cold without their hive. Using temperature and density equations, the model predicts how bees move, generate heat, and form insulating layers. Accurate simulations could reduce harmful field experiments and provide biologists with a powerful tool for studying bee behaviour.

This research quantifies the uncertainty in chaotic systems, showing why long-term predictions — from planetary motion to weather patterns — become unreliable. By developing mathematical models that capture chaotic behaviour, the work supports applications in traffic flow, wireless communication, climate forecasting, and disease spread, revealing why some systems are inherently more predictable than others.