Estimating the state probability distribution for epidemic spreading in complex networks

The problem of state estimation of spreading phenomena in complex networks is considered on the basis of a detectability-based approach. Using a simple, reduced model based state distribution estimator, where the monitored nodes are driven directly by the measured data, asymptotic convergence conditions are provided in terms of the number and location of the required sensors on the basis of the network topology. The convergence of the estimator is established in terms of the largest eigenvalue of a reduced connectivity matrix which stems from removing the monitored nodes and their connections from the original graph. In the case of unit weights, this condition corresponds to measuring the nodes with highest degree. Numerical simulations for a complete and a scale-free network each of 500 nodes and randomly distributed and unit weights, respectively, illustrate the estimator functioning with 20 sensors for the complete, and 38 sensors for the scale-free network.