The ongoing coronavirus disease, also known as COVID-19, has created a global health crisis with also deep social and economic impact. Individual testing has been shown as an an effective non-pharmaceutical intervention of contention of the virus, either on the absence of an effective vaccine or coexisting with one, as vaccines standalone are insufficient to prevent widespread transmission, disease, and morbidity. In a context where COVID tests are scarce, pricey and highly demanded it is key to define policies to optimize the allocation of them while promoting equality among people. In this thesis we will propose different strategies to either statically or dynamically allocate COVID tests among people to contain the spread of the virus while minimizing the number of tests.