We construct differential-integrative equations to investigate the effects of different distributions for the incubation period, defined as the period between receiving of the message and the beginning of the active state, and for the active period, the length of the active state, on the spreading dynamics in a closed system where one member can be dynamically linked to any other with given probability. The evolution of the ensemble-averaged infected rate $\gamma \left(t\right)$ is calculated by solving the equations for various distribution functions. Both the short-term oscillations and long-term saturation crucially depend on the form and parameters of the distribution functions. The obtained results may provide insights into the characteristics of oscillations and a prognosis of a spreading process in closed system.

• Received 11 December 2003

DOI:https://doi.org/10.1103/PhysRevE.69.066102