Aerosol contamination of an aircraft cabin by infectious passengers is a concern of passengers, aircrew and the aviation industry. This may be especially important during a pandemic, such as COVID-19, where the full extent of aerosol transmission is not well understood. A statistical method to determine the number of infectious passengers on board along with a mathematical model estimating the contaminant concentration of aerosols in the cabin and the number of inhaled infectious particles by passengers is presented. An example is used to demonstrated how the results can be estimated during normal operations and emergency conditions with malfunctions of the air conditioning and pressurization system which are responsible maintaining clean cabin air. This type of information can assist the aviation industry in providing the end users of aircraft travel, i.e. passengers and aircrew, with reasonable cabin contaminant guidelines. Accomplishing this in a timely manner requires the combination of modeling adjusted by experimentation. Physically testing all aircraft for each of these conditions would be time consuming, expensive and impractical. Incorporating a model towards solving these problems can serve to bridge the gaps between a finite number of experimental results.