In recent years, advances in small unmanned aerial vehicle (UAV) technology have transformed the use cases of these aircraft from hobby flying to industrial and business applications. These maneuverable, easily deployed tools can be retrofitted with a myriad of sensors and equipment, which make them suitable to perform a variety of specialized tasks. With increasing UAV capabilities, the function of small UAVs can be extended from pure monitoring or surveillance to the dual objective of monitoring an environment for events and addressing the events in some way. This thesis seeks to explore a subdomain of the dual objective problem described, referred to in this thesis as the multi-UAV persistent search and retrieval task with stochastic target appearance (PSR-STA), in which UAVs continuously search an area over a long period of time for targets of interest, which appear according to a probabilistic model, to retrieve and deliver them to a collector location. The advent of high-speed computers and agent-based modeling theory enable the simulation of multi-UAV PSR-STA. However, it can be complicated to combine parts of multi-UAV PSR-STA such as motion models and multi-UAV coordination into one integrated system, and even after they are combined successfully, it is difficult to analyze the system except with simple comparison tools. This thesis 1) proposes a framework that builds a foundation for understanding how to simulate and analyze multi-UAV PSR-STA through prescribing important design decisions and methods for simulation and 2) identifies metrics, analysis tools, and trends related to overall system effectiveness for multi-UAV PSR-STA. A case study of multi-UAV park cleanup is implemented where many simulations with input parameters chosen by a latin hypercube design of experiments are examined, algorithms for choosing the locations of collectors and charging stations based on probabilistic information are proposed, and the differences in effectiveness between four coverage search patterns are analyzed. Measures are highlighted that provide insight into performance variability over time and space. Line charts and the discrete Fourier transform are used to understand temporal patterns inherent in the data. Principal component analysis is used to analyze relevant spatial patterns in effectiveness, and a random forest surrogate model with a profiler is used to explore the non-linear influence of input parameters on the spatial patterns. The trellis chart or figure of figures method is presented for visualizing spatial and temporal data across many simulations. A second set of experiments based on the park cleanup case study are performed and examined to verify the benefits of these methods.