The use of illegal drugs generates a wide range of social harms depending on various ways, according to the policy definition of the problem. The challenge is the way to model the impact of illegal drugs use during a long time period considering the factors that affects the process. Based on these models, estimation could be measured and prediction could be achieved. The illegal drugs use might affect the economic and social structure of the public system leading to direct and effective decisions to overcome the problematic. For that reason, calculation of social cost related to the use of illegal could be introduced over time (t) as a proposed social measure to define the variability of social indicator on society. In this work, a theoretical approach for the calculation of social cost of illegal drugs is proposed and models over time are defined.