The synergy ceiling is determined by clearance of the wild-type population before the single-mutant subpopulation.
(A) Population sizes of the wild-type (, black) and single-drug resistant mutants (, blue) over treatment courses with levels of interaction below, at or above the critical value (). Populations start with sizes and are killed by antibiotics until they are cleared at times and respectively; the overall time of clearance of the infection is simply (orange markers). The interaction level affects the order in which the wild-type and the single-drug resistant subpopulations are eliminated: below the synergy ceiling (, top), the wild-type is eliminated after the single-drug resistant mutant and ; at the synergy ceiling (, middle), the two populations die simultaneously and ; above the synergy ceiling (, bottom), the single-drug resistant mutant outlives the wild-type, such that . Because increasing increases the wild-type killing rate but has no effect on the single-mutant killing rate, efficacy increases with below the synergy ceiling (), but plateaus at and above it (; vertical dashed line: notice that is the same both at and above the synergy ceiling). (B) Increased mutation rates, , give rise to lower . Inset: treatment efficacy, , plateaus at lower levels of drug interaction for higher mutation rates (, blue; , orange; , green; blue and green lines are shifted slightly along y-axis for clarity); values for each line are indicated by vertical dashed lines, and by circles in the main panel. Orange markers indicate the treatment efficacy achieved for different values of when , corresponding to the values in panel A.