A Simple Markovian Spreading Process with Mobile Agents

We investigate a spreading process where each agent is represented by a continuous-time Markov chain with two states, L and M. State L refers to “home,” whereas state M refers to a “meeting place.” When two agents stay together at M, they “meet” and form a contact. This means, according to the application, that they can exchange information, infect each other, perform an act of trade, and so on. We assume that initially all are at state L, and exactly one of the agents possesses a piece of information (or is infected by a contagious disease, etc.) The process can generally be classified as a spreading process with mobile agents, and its simplicity allows us to demonstrate several interesting properties. We provide an efficient way for computing the propagation time and investigate the dependence of the spreading process on parameters such as the number of agents, the number of uninformed agents at the end of the process, and the contact intensity.