Several recent studies have proposed an automatic plant disease identification system based on deep learning. Although successful, these approaches are generally based on learned classification models with target classes of joint host species-disease pairs that may not allow optimal use of the available information. This is due to the fact that they require distinguishing between similar host species or diseases. In fact, these approaches have limited scalability because the size of a network gradually increases as new classes are added, even if information on host species or diseases is already available. This constraint is all the more important as it can be difficult to collect/establish a specific list of all diseases for each host plant species in an actual application. In this paper, we address the problems by proposing a new conditional multi-task learning (CMTL) approach which allows the distribution of host species and disease characteristics learned simultaneously with a conditional link between them. This conditioning is formed in such a way that the knowledge to infer the prediction of one concept (the diseases) depends on the other concept (the host species), which corresponds to the way plant pathologists used to infer the diseases of the host species. We show that our approach can improve the performance of plant disease identification compared to the usual species-disease pair modeling in the previous studies. Meanwhile, we also compose a new dataset on plant disease identification that could serve as an important benchmark in this field.