Infection.

Many models of bacterium-phage interaction assume that a mass action process governs infection (41, 44), but P. aeruginosa-phage infection rates are not well approximated by a mass action process (74, 75). More realistically, infection rates decrease as population growth activates quorum-sensing and biofilm formation (76). One way to accommodate this infection process is to replace a mass action term with a Michaelis-Menten or Hollings type II functional response. In this case, all infection and absorption rates are proportional to the nonlinear response

where V is the phage of interest, B is the bacterium of interest, and h_η is the bacterial population at which the infection rate is half of the maximum. For small bacterial populations (B ≈ 0), infection is approximately a mass action process. As the bacterial population grows, the infection rate saturates (Fig. 9a).

Sketches of the functions for infection r(V,B) with phage density V = 10 (a), antibiotic stress s(t,{t_i}) with {t_i} = {5,15} (b), phage production b(s) (c), and cell reproduction multiplier g(s) (d). Parameter values are taken from the baselines in Table 2.