This paper uses movement as a marker to study interactions in humans and animals to better understand their collective behaviors. Interaction is an important driving force in social and ecological systems. It can also play a significant role in the transmission of infectious diseases and viruses as witnessed during the ongoing COVID-19 pandemic. Although a number of approaches have been developed to analyze interaction using movement data sets, these methods mainly capture concurrent and dyadic interaction (i.e. when two individuals have direct contact or move synchronously in the spatial proximity of each other). Less work has been done on tracing interaction between multiple individuals, especially when the interaction occurs with a delay or via indirect contact (i.e. when individuals visit the same location asynchronously). This paper introduces a new Object-oRiented Time-Geographic Analytical approach (ORTEGA) to extract concurrent and delayed interaction patterns between individuals in space and time. The method leverages the time-geography framework to incorporate the effects of uncertainty and gaps in movement data in the analysis of interaction and tracing contact patterns. Using two different case studies and real GPS tracking data, the method is evaluated in (1) detecting patterns of dyadic, intra and interspecific interactions between two apex predators, tigers and leopards in Thailand; and (2) tracing potential contacts between a large group of individuals of the same and different households in San Jose, California. The results indicate that tigers and leopards have an awareness of each other and their interaction is mainly indirect and delayed. In the human context, the results show that while individuals of the same household have more concurrent interaction, members of different households follow similar patterns asynchronously exhibiting delayed interaction. The delayed interactions and potential asynchronous contacts are often underestimated by the common digital contact tracing technologies. With this study we show how a generic method can be used to identify interesting movement patterns across the human and animal divide.