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Taking the context of simulating a retail environment using agent basedmodelling, a theoretical model is presented that describes the probabilitydistribution of customer "collisions" using a novel space transformation to theTorus $Tor^2$. A method for generating the distribution of customer paths basedon historical basket data is developed. Finally a calculation of the number ofsimulations required for statistical significance is developed. Animplementation of this modelling approach to run simulations on multiple storegeometries at industrial scale is being developed with current progressdetailed in the technical appendix.

Simulating human interactions in supermarkets to measure the risk of COVID-19 contagion at scale