The transport and dispersion of respiratory droplets arising from human cough is investigated in the present work. A mathematical model based on mass, momentum and energy conservation equations of a Lagrangian particle is employed to track individual respiratory droplets in a constant carrier flow. The objective of the present study is to account for the cloud evaporation effect, due to which the evaporation rate of neighbouring droplets is significantly reduced when the inter-droplet distance is small. In addition, to verify the potential of the current model to predict the droplet transport process, the results are compared against the Lagrangian Discrete Phase Model (DPM), wherein the surrounding gas flow is computed through the Reynolds Averaged Navier-Stokes (RANS) equations. The influence of ambient conditions like coflow, temperature and relative humidity on the transport process is also investigated.