Stability of Spreading Processes with General Transmission and Recovery Times
Although viral spreading processes taking place in networks are commonly analyzed using Markovian models in which both the transmission times and the recovery times follow exponential distributions, empirical studies show that, in most real scenarios, the distribution of these times are far from exponential. To overcome this limitation, we first introduce a generalized spreading model that allows for transmission and recovery times to follow arbitrary distributions within an arbitrary accuracy. In this context, we derive conditions for the generalized spreading process to converge towards the disease-free equilibrium (in other words, to eradicate the viral spread) without relying on mean-field approximations. Based on our results, we illustrate how the particular shape of the transmission/recovery distribution heavily influences the boundary of the stability region of the spread, as well as the decay rate inside this region. Therefore, modeling non-exponential transmission/recovery times observed in realistic spreading processes via exponential distributions can induce significant errors in the stability analysis of the dynamics.