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Based on previous work done in this field, we build a dynamical system thatdescribes changes in drug addiction in an isolated population when twoaddictive substances are available simultaneously. We then use our model toinvestigate whether the system captures the process of users switching drughabits. One of the motivations for this project is to mathematically check theconjecture that being addicted to a less-addictive substance will effectivelylead individuals to become dependent on more addictive and potentially moredangerous drugs.  We introduce additional assumptions, under which our model is reduced to acompetitive Lotka-Volterra system. This dynamical system has three or fourfixed points, stability of which then gives an implication about the outcomesof the competition between addictive substances and, therefore, the fate ofindividuals in the population. From the analysis of the reduced model, wedetermine that there actually exist parameter regimes that capture thefollowing dynamics: depending on the initial distribution of the drugpreference; either the use of both drugs will die out, the usage of one of thedrugs will become prevalent, or addictions to both drugs will coexist.

Mathematical Modeling of Drug Use: The Dynamics of Monosubstance Dependence for Two Addictive Drugs