  We theoretically study noise-induced phase switch phenomena in an inertial
majority-vote (IMV) model introduced in a recent paper [Phys. Rev. E 95, 042304
(2017)]. The IMV model generates a strong hysteresis behavior as the noise
intensity $f$ goes forward and backward, a main characteristic of a first-order
phase transition, in contrast to a second-order phase transition in the
original MV model. Using the Wentzel-Kramers-Brillouin approximation for the
master equation, we reduce the problem to finding the zero-energy trajectories
in an effective Hamiltonian system, and the mean switching time depends
exponentially on the associated action and the number of particles $N$. Within
the hysteresis region, we find that the actions along the optimal forward
switching path from ordered phase (OP) to disordered phase (DP) and its
backward path, show distinct variation trends with $f$, and intersect at
$f=f_c$ that determines the coexisting line of OP and DP. This results in a
nonmonotonic dependence of the mean switching time between two symmetric OPs on
$f$, with a minimum at $f_c$ for sufficiently large $N$. Finally, the
theoretical results are validated by Monte Carlo simulations.
