Advanced persistent distributed denial-of-service (APDDoS) attack is a serious threat to the computer network's security. This paper proposes a new APDDoS model integrated with a reverse-path forwarding based defensive strategy. The attacked threshold of the attached model is calculated and the model's stability under different conditions is analytically analyzed. The impact of different parameter values on the system's behaviors is investigated and practical strategies to mitigate the APDDoS attack are recommended. INDEX TERMS Distributed denial-of-service attack, defensive strategy, dynamical model, stability, numerical simulations.