Locating the source of interacting signal in complex networks

We investigate the problem of locating the source of a self-interacting signal spreading in a complex networks. We use a well-known rumour model as an example of the process with self-interaction. According to this model based on the SIR epidemic dynamics, the infected nodes may interact and discourage each other from gossiping with probability $α$. We compare three algorithms of source localization: Limited Pinto-Thiran-Vettarli (LPTV), Gradient Maximum Likelihood (GMLA) and one based on Pearson correlation between time and distance. The results of numerical simulations show that additional interactions between infected nodes decrease the quality of LPTV and Pearson. GMLA is the most resistant to harmful effects of the self-interactions, which is especially visible for medium and high level of stochasticity of the process, when spreading rate is below 0.5. The reason for this may be the fact that GMLA uses only the nearest observers, which are much less likely affected by the interactions between infected nodes, because these contacts become important as the epidemics develops and the number of infected agents increases.