We investigate the asymptotic performance of a reward incentive Delay Tolerant Network based on mean field limit. We consider a two-hop network with one source and one destination and N relays. The source is backlogged and sends messages to the destination by forwarding to the relays it meets. For each message, there is a promised reward for the first one who successfully transmits it to the destination. It was shown in a previous work, the optimal policy for the relays is of thresholds type (a relay will accept a message until certain time and drop it after a second threshold). When the second threshold in infinite, we give the mean-field ODE and show that all the messages have the same probability of success. When the second threshold is finite we only give an ODE approximation since the dynamics are not Markovian.