Modeling indoor dispersion is an important problem for risk analysis used to justify design improvements that increase safety. Of particular interest is a method to estimate what fraction of the volume of a room could have flammable concentrations when the source rate is too weak to fill the entire room. An analytic model is described here that allows a time-varying source rate such as typically occurs with an evaporating liquid pool. The model allows automatic increases and decreases in the ventilation rate and/or fresh air makeup ratio such as could be activated by a gas sensor systems. This provides a design tool for such gas sensor systems. An approximate approach is developed to estimate the effects of imperfect mixing, such as can occur with density stratification or dead zones. Two options are described, a dead zone model and a "bypass" model.