We consider a Delay/Disruption Tolerant Network under two-hop routing. Our objective is to estimate and track the degree of spread of a message/file in the network. Indeed, having such real-time information is critical for on-line control of routing and energy expenditure. It also benefits the multi-casting application. With exponential inter-meeting times of mobile nodes: (i) for the estimation problem, we obtain exact expressions for the minimum mean-squared error (MMSE) estimator, and (ii) for the tracking problem, we first derive the diffusion approximations for the system dynamics and the measurements and then apply Kalman filtering. We also apply the solutions of the estimation and filtering problems to predict the time when a certain pre-defined fraction of nodes have received a copy of the message/file. Our analytical results are corroborated with extensive simulation results.