We show that the dynamics of the expiratory cloud ejected during human respiratory events can be modeled by extending the theory of buoyant vortex rings with an initial momentum. We embed the integral conservation laws that govern the cloud's motion into the model of an expanding vortex to determine the velocity field inside and outside the cloud. We then apply a Lagrangian particle-tracking model to calculate the trajectories of the mucosalivary droplets suspended within the cloud. Our results show very good agreement with the available experimental data. The vortex is shown to have a significant effect on suspending the droplets present in the cloud, increasing the time they remain airborne and extending their range further than predicted by the existing models. We also study the role that initial conditions have on the maximum streamwise range of the droplets, finding that decreasing the angle of projection can reduce the spread of the droplets by an order of meters. Finally, we discuss the importance of these findings in the context of informing public health policies and global information campaigns to slow down the spread of respiratory viruses.