Viruses can remain infectious in the aerosolized solid residue left upon the evaporation of respiratory droplets for very long times. However, the precise mechanisms that allow viral particles to endure the harsh physicochemical conditions found in these drops for so long are poorly understood. In this talk we present our ongoing theoretical and experimental study on the transport of solutes and viral particles inside evaporating complex drops, with the aim to elucidate the precise physicochemical mechanisms that ultimately lead to viral inactivation. In the first part of the talk we present a model of the evaporation-driven hydrodynamics of complex drops containing water, salt, and a glycoprotein (mucin). In the second part of the talk, we apply this model to explain the spatial distribution of viral particles in the dry residue of a sessile drop that we have observed experimentally.