The Justinianic Plague, the first part of the earliest of the three plague pandemics, has minimal historical documentation. Based on the limited primary sources, historians have argued both for and against the "maximalist narrative" of plague, i.e. that the Justinianic Plague had universally devastating effects throughout the Mediterranean region during the sixth century CE. Using primary sources of one of the pandemic's best documented outbreaks that took place in Constantinople during 542 CE, as well as modern findings on plague etiology and epidemiology, we developed a series of dynamic, compartmental models of disease to explore which, if any, transmission routes of plague are feasible. Using expected parameter values, we find that the bubonic and bubonic-pneumonic transmission routes exceed maximalist mortality estimates and are of shorter detectable duration than described by the primary sources. When accounting for parameter uncertainty, several of the bubonic plague model configurations yielded interquartile estimates consistent with the upper end of maximalist estimates of mortality; however, these models had shorter detectable outbreaks than suggested by the primary sources. The pneumonic transmission routes suggest that by itself, pneumonic plague would not cause significant mortality in the city. However, our global sensitivity analysis shows that predicted disease dynamics vary widely for all hypothesized transmission routes, suggesting that regardless of its effects in Constantinople, the Justinianic Plague would have likely had differential effects across urban areas around the Mediterranean. Our work highlights the uncertainty surrounding the details in the primary sources on the Justinianic Plague and calls into question the likelihood that the Justinianic Plague affected all localities in the same way.