Cumulative mutant virus load versus mutation rate, <i>u</i>₁, during treatment.

The cumulative mutant virus load increases with mutation rate u1 before reaching a peak and then decreases to low values. If the peak is reached at a mutation rate that is less than the natural mutation rate, u0 (red dotted line), then any increase in mutation rate reduces the cumulative mutant load. If the peak is reached for a mutation rate greater than u0, then the increase in mutation rate caused by mutagenic treatment must exceed a threshold value (blue dotted line) to reduce the cumulative mutant virus load. We also consider mutants with a 1% advantage in the birth rate. As expected, we observe a higher cumulative mutant load for the advantageous mutant (green line) compared to the neutral mutant (blue line). But the minimum mutation rate under treatment that is required for evolutionary safety is slightly lower for the advantageous mutant. (A) Treatment starts at peak virus load. (B) Treatment starts at infection. The red arrow indicates the mutation rate at the error threshold of the growth phase. Parameters: b = 7.61 per day, a0 = 3 per day, n = 1 position, T = 5 days, m and a1 as shown. The code used to generate this figure can be found at DOI: 10.5281/zenodo.8017992.