The most common and effective pest control methodology for insect pests in grain storage is fumigation with phosphine gas. However the emergence of strong levels of resistance to phosphine threatens its continued use. Linkage analysis and molecular techniques have provided strong evidence that resistance is conferred by two genes on separate chromosomes. For the insect pest *Rhyzopertha dominica* (the lesser grain borer) resistance in individuals homozygous for both resistant genes has been determined to be well over 250 times greater than those with no copies of the resistance genes, whereas there are weaker resistance factors of 2.5 times to 30 times if the resistance genes are present in only one of the two locations, depending on which location.

This paper describes the development of a mathematical model for the population genetics for *Rhyzopertha*, for fumigation under a given concentration of phosphine gas. The mathematical model incorporates two-locus genetics, with nine genotypes, modelled by differential equations. Using the model, some different fumigation strategies are investigated; for fumigation switched on for a given period and switched off for a given period. The two-locus model is compared with a single-locus model by aggregating the genotypes in the two-locus model. While this model is still in the preliminary stages and requires more rigorous validation, it does clearly demonstrate much different qualitative outcomes for the two-locus model compared to an a one-locus approach. It is argued that accounting for the correct genetics is crucial.