The production cross sections for the medical isotope $^{99}\mathrm{Mo}$ were measured using the $^{100}\mathrm{Mo}(n,2n)$ reaction at average neutron energies of $10.95\ifmmode\pm\else\textpm\fi{}0.45, 13.97\ifmmode\pm\else\textpm\fi{}0.68, 16.99\ifmmode\pm\else\textpm\fi{}0.53$, and $20.00\ifmmode\pm\else\textpm\fi{}0.58$ MeV using offline $\ensuremath{\gamma}$-ray spectroscopy. The neutron beam was generated using the $^{\mathrm{nat}}\mathrm{Li}(p,n)$ reaction at the 14UD BARC-TIFR Pelletron facility, Mumbai, India. The uncertainties in the measured data were calculated using covariance analysis. The experimental results were compared with the existing data libraries ENDF/B-VII.1, JENDL-4.0, JEFF-3.2, and CENDL-3.1. The present results were also reproduced and compared with the theoretical nuclear model codes talys-1.9 and alice-2017 using different input descriptions. A modified set of parameters were also used in talys-1.9 to fit the existing data more accurately. The present findings show a good agreement with the theoretical predictions and with the existing experimental results from the different data libraries. In addition to this, a comparative study have also been performed between the literature data of $(n,p), (n,2n)$, and $(n,\ensuremath{\alpha})$ reaction cross sections at 14.5 MeV using various systematic formulas. The outcomes of the present work are important for the advancement of medical accelerators, dosimetry, and fast reactor systems.