Geometrical constructions and analysis in population capture cohorts

In this article, fundamental results on the formation of population capture cohorts using analysis, probability, and geometric arguments are derived. Capture cohort formation is studied in the article without a disease framework. The central framework draws inspiration from insect ecology or animal ecology and demography where the age of individuals, birth rates and distribution of time from disease to death are often unknown. Through geometric intuition and cohort formulations it is tried here improving our understanding of the longitudinal cohort data. The capture cohorts constructed here facilitates our analysis of the speed at which cohorts form, while ensuring that individuals do not overlap within cohorts. Such constructions improved our intuition on survival probabilities of cohorts. This article introduces original ideas by connecting the geometry of paths of cohort formations with methods of data analysis, probability, and mathematical analysis. Two functions that are linked through their domains are introduced and measurable function properties are proved. These functions helped to draw paths in the XY-plane. We also investigate the probability of capturing sub-cohorts within a specified time interval. The occurrence of an event of interest in a random experiment can be modeled using geometric distribution. It is shown that the shape of the formation of a cohort and the timings of the occurrence of the first captured individual in the population are related.