The environmental consequences of lead ion accumulation have been linked to detrimental health impacts in humans. Hence, removal of heavy metal (lead, Pb) ions by membrane adsorption/filtration was studied in this work using nanofibrous membranes in which the adsorbent metal-organic framework, MOF-808, was embedded. S-shaped breakthrough curves were obtained experimentally when the heavy metal concentration in the permeate was plotted vs the filtration period. Simple model equations that enable the reproduction of the S-shaped breakthrough curve were derived. It was found that the model equations could simulate the experimental data reasonably well. Attempts were further made to correlate the parameters involved in the model equations to the properties of mixed matrix nanofibrous membranes, including the pore size and pore size distribution, membrane thickness, fiber diameter, the adsorption rate constant, the Langmuir adsorption constant and the maximum adsorption capacity. The model equation parameters were also correlated to the operating conditions including the heavy metal concentration in the feed and the transmembrane pressure difference. It is believed that the model equations, despite this simplicity, can provide deeper insight into the membrane adsorption/filtration phenomena. These equations also contribute to the process design for successful removal of heavy metal ions from the environment to improve health factors for humans.