Materials contained in plastic packages can transfer (migrate) into the contents. In some circumstances, such as packages of food, drink or medicine, the consequences of this migration can be unpleasant or even harmful. Many countries, and the European Community, have adopted legal regulations designed to limit the amount of migration. It is shown, partly by discussing one example in some detail, that certain quantitative criteria in such regulations are unsatisfactory. The reasons include (
a
) improper recognition of the importance of package geometry, (
b
) invalid assumptions about a correspondence between concentrations in the contents and mass transfer per unit area of the package-contents interface and (
c
) failure to account, in an adequate manner, for the inevitable variability between nominally identical package systems. The principal theme of the paper is that these faults could have been, and can be, substantially ameliorated by proper use of mathematical models. Common shortcomings in the previous (but very limited) use of mathematics are exposed partly by detailed examination of a recent research paper. The paper discusses the requirements of a successful model and considers the simplest type, namely diffusion equations with diffusion coefficients that are independent of the concentrations of the migrant in either the plastic or the contents. Particular solutions are chosen to illustrate faults in existing legislation and practice, and because they are thought to be good candidates for testing against data. It is argued that future experiments would be more successful and more useful if they were planned and conducted in teams involving mathematicians.
Simple mathematical models for controlling COVID-19 transmission through social distancing and community awareness