Population count is both a Nation's resource and driver of public policy analysis decision-making. This report derives, summarizes, and calculates simple continuous, as well as, discrete accounting life tables. New bio-mathematical approaches and applications of differential equations, of probability and random processes, and of fractional calculus to competing species as people chemistry or population kinetics with numerous applications to human behaviors, to ecological dynamics, to Lotka-Volterra equations' modifications, and to epidemiological modeling are presented. The collection of petite researches relies on undergraduate mathematical studies with data and computation.