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$\quad \Gamma_x \equiv $ combined invasion rate per attached bacteria, per host cell $ = \Gamma_v + Gamma_c$  \noindent %\noindent  There is evidence that suggests a physical limit to the number of ruffles per cell $\tilde{r}_{\rm max}$, and the number of invaded bacteria per cell $\tilde{b}_{x, \rm max}$, so we define the following effective rates. \noindent There is evidence that suggests a physical limit to the number of invaded bacteria per cell $\tilde{b}_{x, \rm max}$, so we define the following effective rate.  $\Gamma_r^{*} %$\Gamma_r^{*}  (t) \equiv $ effective (limited) ruffle formation rate per attached bacteria $ = \Gamma_r (1 - \frac{\tilde{r} (t)}{\tilde{r}_{\mathrm{max}}})$ $\Gamma_x^{*} (t) \equiv $ effective (limited) invasion rate per attached bacteria $ = \Gamma_x (1 - \frac{\tilde{b_x} (t)}{\tilde{b}_{x, \mathrm{max}}})$