Bacterial Resistance And The Optimal Use Of Antibiotics

In recent years bacteria have become increasingly resistant to antibiotics, leading to a decline in the effectiveness of antibiotics in treating infectious disease. This paper uses a framework based on an epidemiological model of infection in which antibiotic effectiveness is treated as a nonrenewable resource. In the model presented, bacterial resistance (the converse of effectiveness) develops as a result of selective pressure on non-resistant strains due to antibiotic use. When two antibiotics differ only in quality, it is optimal to use one antibiotic initially, following which it is optimal to switch to a combination of the two drugs. The optimal proportion and timing of use for the two antibiotics depends precisely on the difference between the rates at which bacterial resistance to each antibiotic evolves and on the differences in their pharmaceutical costs, results that are unique in the literature on antibiotic resistance. We use standard numerical techniques to illustrate cas..