Birth and death rates in the four studied scenarios.

The overall birth and death rates, denoted by λj and μj, are composed of the birth, death and competition processes that occur at rates βj, δj and γj, respectively. Additionally, the effect of antibiotics, denoted by αj(c), affects either the birth or the death rate, depending on the type of drug administered. The variable c denotes the concentration of the antibiotic and the index j indicates the strain-specificity, j = S or j = R for antibiotic-sensitive or -resistant cells.