(A) The viral dynamics after the initiation of a treatment with bNAb infusion () is determined by two competing processes. Susceptible strains (sus) undergo exponential decay (red line) with decay rate given by , while the resistant mutants (mut) undergo logistic growth back up to the carrying capacity () of the patient. In the deterministic limit (Equation 1), the rebound time is linearly related to the log-frequency of the mutant fraction. (B) The schematic shows the four stochastic processes of birth, death, mutation, and neutralization with their respective rates for susceptible (purple) and resistant (blue) variants. These processes define the evolution of a viral population. Note that both the susceptible and the resistant variants are subject to birth and death with their respective rates. (C) The birth and death rates can be visualized as a region of size which is partitioned into birth and death events. In the absence of antibodies, the susceptible population has balanced birth and death rates, , while the resistant population has a negative net birth rate equal to the fitness difference . After introduction of the antibody, the susceptible population decays at rate , and without competition from the susceptible population, the resistant population grows at the free growth-rate . (D) Mutational target size is inferred a priori from the genotype-phenotype mapping, which can be visualized as a bipartite graph. The nodes correspond to codons, while the edges are the mutations which link one codon to another, weighted according to the respective mutation rates. The average edge weight from codons of susceptible variants to the escape mutants determines the rate of escape mutations . Mutations can be divided into two types: transitions (black) are within-class, and transversions (red) are out of class nucleotide changes. Transitions occur at about 8 times higher rate than transversions (Figure 2). (E) A coarse grained fitness and mutation model for two of the escape sites (281 and 282) against antibody 3BNC117 are shown. Left: At each escape mediating site, amino acids fall into one of three groups: (i) susceptible (wild-type), (ii) escape mutant, and (iii) fatal. For an escape-class amino acid at site the virus incurs a fitness cost , and these costs are additive across sites. Right: Mutations at a given site occur with (independent) forward and backward rates which govern the substitution events between amino acid classes.