Experimentalists use particles as tracers in liquid helium. The intrusive effects of particles on the dynamics of vortices remain poorly understood. We implement a study of how basic, well understood vortex states, such as a propagating pair of oppositely signed vortices, change in the presence of particles by using a simple model based on the Magnus force. We focus on the two-dimensional case, and compare the analytic and semianalytic models with simulations of the Gross-Pitaevskii (GP) equation with particles modeled by dynamic external potentials. The results confirm that the Magnus force model is an effective way to approximate vortex-particle motion either with closed-form simplified solutions or with a more accurate numerically solvable ordinary differential equations. Furthermore, we increase the complexity of the vortex states and show that the suggested semianalytical model remains robust in capturing the dynamics observed in the GP simulations.