The emergence and reemergence of coronavirus epidemics sparked renewed concerns from global epidemiology researchers and public health administrators. Mathematical models that represented how contact tracing and follow-up may control Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS) transmissions were developed for evaluating different infection control interventions, estimating likely number of infections as well as facilitating understanding of their likely epidemiology. We reviewed mathematical models for contact tracing and follow-up control measures of SARS and MERS transmission. Model characteristics, epidemiological parameters and intervention parameters used in the mathematical models from seven studies were summarized. A major concern identified in future epidemics is whether public health administrators can collect all the required data for building epidemiological models in a short period of time during the early phase of an outbreak. Also, currently available models do not explicitly model constrained resources. We urge for closed-loop communication between public health administrators and modelling researchers to come up with guidelines to delineate the collection of the required data in the midst of an outbreak and the inclusion of additional logistical details in future similar models.