Advanced Calculus in Mortality Modelling: Exploring Survival, Hazard and Longevity Forecasting

This thesis presents a comprehensive exploration of mortality dynamics, survival analysis, population ageing, epidemiological modelling, longevity inequality, and health economics. It integrates mathematical foundations with intuitive explanations designed to make complex ideas accessible without reducing academic rigor. The work develops survival and hazard functions from first principles, applies Gompertz and Makeham mortality models, constructs mortality forecasts, analyses demographic ageing, examines disease-driven mortality patterns, and evaluates inequality in longevity outcomes. The thesis concludes with integrated policy implications and a brief note on how actuaries may apply these models in future risk assessments.