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\subsection{Bacterial attachment}  The change in the fraction of host cells withattached  bacteria $a$ $h$  will only depend on the primary attachment rate $\Gamma_a$ and not secondary attachment (ruffle recruitment) rate  $\Gamma_b$, because for bacteria to be recruited by ruffles, a bacterium has already attached to form that ruffle. Of course, this This  rate of change will be limited by the bacterial density, $\rho_B$. density $\rho_B$ and by the fraction of host cells without bacteria.  \begin{equation}  \dot{a} \dot{h}  = \frac{\dot{H}_a}{H} \frac{\dot{H}}{H_{\rm tot}}  = \frac{H \frac{H_{\rm tot}  - H_a}{H} H}{H_{\rm tot}}  \Gamma_a \rho_B = (1-a) (1-h)  \Gamma_a (1-b) \frac{mc}{A} \end{equation}  It is important to note that bacterial invasion/entry is not a consideration in the above equation. Consequently, if all the bacteria attached to a host cell have invaded, we still consider that host cell to have attached bacteria, even though it has no extracellular bacteria left.