Host shifts can cause novel infectious diseases, and is a key process in diversification. Disentangling the effects of host shift vs. those of cospeciation is non-trivial as both can result in phylogenic congruence. We develop a new framework based on network analysis and Approximate Bayesian Computation to quantify host shift and cospeciation rates in host-parasite systems. Our method enables estimation of the expected time to the next host shift or cospeciation event. We then apply it to avian haemosporidian parasite systems and to the pocket gophers-chewing lice system, and demonstrate that both host shift and cospeciation can be reliably estimated by our method. We confirm that host shifts have shaped the evolutionary history of avian haemosporidian parasites and have played a minor role in the gopher-chewing lice system. Our method is promising for predicting the rate of potential host shifts and thus the emergence of novel infectious diseases.