We describe seismic monitoring and modeling of an active volcano for the purpose of predicting the magma transport process in real time. We selected the Piton de la Fournaise, which has been monitored by an observatory since the early 1980s, and is active, with 28 eruptions from 1980 until August 1992. It erupted on March 9, 1998, after an unusually long quiet period. The eruption lasted until September 21, 1998. Before the March eruption, we completed the initial construction of a model of a magma system based primarily on long-period (LP) events and coda localization. We found that LP events are associated with the lateral movement of magma to the rift zone and not with the vertical movement to the summit. We also found that the source of 2 Hz LP events is located below that of 1 Hz LP events. The coda localization is a newly discovered phenomenon that helped to locate a magma body. This model was used for interpreting the incoming information from the precursory seismic crisis and the eruption tremor during the 6 months of the eruption. The simultaneous monitoring and modeling of an active volcano led us to a quantitative simulation of the eruption process, computing excess pressure and flow rate in a system of reservoirs connected by channels.