To understand the regulatory pathways underlying diseases, studies often investigate the differential gene expression between genetically or chemically differing cell populations. Differential expression analysis identifies global changes in transcription and enables the inference of functional roles of applied perturbations. This approach has transformed the discovery of genetic drivers of disease and possible therapies. However, differential expression analysis does not provide quantitative predictions of gene expression in untested conditions. We present a hybrid approach, termed DiffExPy, that uniquely combines discrete, differential expression analysis with in silico differential equation simulations to yield accurate, quantitative predictions of gene expression from time-series data.