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A model combines demographic data provided by the United States Census Bureau for 2021 with survey data on sexual activity from the Centers for Disease Control and Prevention to estimate the structure by age and sex of the sexually active population in the United States. It also provides the proportions of newly sexually active people by age and sex. The model is based on percentages of sexually active people by age and sex, and on an ordinary differential equation formalizing a “learning process” for the years 2009 to 2019. The data produced fit well with the empirical data for each age and sex. 

Social hierarchies are ubiquitous in social groups such as human societies and social insect colonies; however, the factors that maintain these hierarchies are less clear. Motivated by the shared reproductive hierarchy of the ant species Harpegnathos saltator, we have developed simple compartmental nonlinear differential equations to explore how key life-history and metabolic rate parameters may impact and determine its colony size and the length of its shared hierarchy. Our modeling approach incorporates nonlinear social interactions and metabolic theory. The results from the proposed model, which were linked with limited data, show that: (1) the proportion of reproductive individuals decreases over colony growth; (2) an increase in mortality rates can diminish colony size but may also increase the proportion of reproductive individuals; and (3) the metabolic rates have a major impact in the colony size and structure of a shared hierarchy. 

Risk has been a key factor influencing trust in Human-Automation interactions, though there is no unified tool to study its dynamics. We provide a framework for defining and assessing relative risk of automation usage through performance dynamics and apply this framework to a dataset from a previous study. Our approach allows us to explore how operators’ ability and different automation conditions impact the performance and relative risk dynamics. Our results on performance dynamics show that, on average, operators perform better (1) using automation that is more reliable and (2) using partial automation (more workload) than full automation (less workload). Our analysis of relative risk dynamics indicates that automation with higher reliability has higher relative risk dynamics. This suggests that operators are willing to take more risk for automation with higher reliability. Additionally, when the reliability of automation is lower, operators adapt their behavior to result in lower risk.