Dynamics and asymptotical behavior of spreading processes in a closed system.
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(t) 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.
Xiong
Shi-Jie
SJ
Department of Physics, Nanjing University, Nanjing 210093, China.