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This book introduces and applies the stochastic modeling techniques and the first exit time theory in demography through describing the theory related to the health state of a population and the introduced health state function. The book provides the derivation and classification of the human development stages. The data fitting techniques and related programs are also presented. Many new and old terms are explored and quantitatively estimated, especially the health state or "vitality" of a population, the deterioration and related functions, as well as healthy life expectancy. The book provides the appropriate comparative applications and statistics as connecting tools accompanied by the existing literature, and as such it will be a valuable source to demographers, health scientists, statisticians, economists and sociologists.