Abstract
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.
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Schinazi, R.B. On the Spread of Drug-Resistant Diseases. Journal of Statistical Physics 97, 409–417 (1999). https://doi.org/10.1023/A:1004635606196
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DOI: https://doi.org/10.1023/A:1004635606196