On the spread of drug resistant diseases

We introduce an interacting particle system to model the emergence of drug resistant diseases, one of the most serious health problems in modern society. We are interested in diseases for which a natural strain may mutate into a drug resistant strain. This happens, for instance, when antibiotics are misused. The main result of our analysis is that with an efficient drug against the natural strain, if there is even a small chance that the natural strain mutates into the drug resistant one, then there will eventually be an outbreak of the drug resistant strain throughout the population. In that case the natural strain disappears and is replaced by the drug resistant strain. The disturbing part of this is that an efficient treatment of the natural strain gives an edge to the drug resistant strain.