Drug resistance in an age-of-infection model

In the case of a disease spreading over a time-scale comparable to the average lifetime in a host population, when the infectiousness of individuals depends on the tine since the onset of infection and when infections involve both drug-sensitive and drug-resistant strains of a pathogen, resistance may develop during the treatment of drug-sensitive strains. If increasing the treatment rate reduces the reproduction number of the drug-sensitive strain to a value below the reproduction number of the drug-resistant strain, then the disease may persist at a boundary equilibrium where only drug-resistant infection is present.