Mathematical analysis of agent swarm behavior in an agent-based electronic health record system

System behavior, in a multi-agent system, can be difficult to predict and often, unexpected system behaviors will occur which lead to poor system performance. These unexpected system behaviors result from unforeseen group actions of agent groups, and agent-group behavior that is not directly coded by the agent designers. This paper presents a mathematical model to analyze agent swarm behavior in an agent-based system. Our mathematical model is composed of a set of differential equations, which will be the main focus of our study into agent dynamics and complex systems. We demonstrate our mathematical model by applying it to an agent-based health record system (ABHRS). The ABHRS is an electronic health record system which is enhanced using mobile agent technology. The main idea of the ABHRS is to allow patient health records to autonomously move through a computer network uniting scattered and distributed data into one consistent and complete data set or patient health record. ABHRS is an example of multi-agent swarm system, which composed of many simple agents and a system that is able to self-organized. A prototype ABHRS was developed in this work using TEEMA (TRLabs execution environment for mobile agents) platforms and experimental results using this prototype are presented. Our experimental results suggest that the ABHRS will in fact have predictable attributes such as growing clusters of mobile agents at Doctor, Pharmacy and Lab sites. In addition, our numerical (experimental) results closely match those of our theoretical model for the system