  Monolayer transition metal dichalcogenides (TMDCs), like MoS$_2$, MoSe$_2$,
WS$_2$, and WSe$_2$, feature direct bandgaps, strong spin-orbit coupling, and
exciton-polariton interactions at the atomic scale, which could be harnessed
for efficient light emission, valleytronics, and polaritonic lasing,
respectively. Nevertheless, to build next-generation photonic devices that make
use of these features, it is first essential to model the all-optical control
mechanisms in TMDCs. Herein, a simple model is proposed to quantify the
performance of a 35$\,$\textmu m long Si$_3$N$_4$ waveguide-integrated
all-optical MoSe$_2$ modulator. Using this model, a switching energy of
14.6$\,$pJ is obtained for a transverse-magnetic (TM) and transverse-electric
(TE) polarised pump signals at $\lambda =\,$480$\,$nm. Moreover, maximal
extinction ratios of 20.6$\,$dB and 20.1$\,$dB are achieved for a TM and TE
polarised probe signal at $\lambda =\,$500$\,$nm, respectively, with an
ultra-low insertion loss of $<0.3\,$dB. Moreover, the device operates with an
ultrafast recovery time of 50$\,$ps, while maintaining a high extinction ratio
for practical applications. These findings facilitate modeling and designing
novel TMDC-based photonic devices.
