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During the time course of invasion by \textit{Salmonella}, a bacterium can be in 4 different generalized stages: swimming (looking to attach to a host) $B$, attached to a host cell $B_a$, invaded and vacuolar $B_v$, or invaded and cytosolic $B_c$. The counts of bacteria in these stages are constantly changing in time, but ignoring xenophagy and replication, the total number will remain constant:  \begin{equation}  $B_{\rm B_{\rm  tot} = B(t) + B_a(t) + B_x(t) + B_c(t)$ B_c(t)  \end{equation}  We classify the relationship between host cells and bacteria in one of three ways: host cells with no bacteria $H$, with attached bacteria $H_a$, with invaded vacuolar bacteria $H_v$, and with invaded cytosolic bacteria $H_c$. A host cell may have a combination of attached, vacuolar and cytosolic bacteria at one time, so the total number of host cells is the the length of the union of these sets:  \begin{equation}  $H_{\rm H_{\rm  tot} = \left\vert{ \left\{H(t) \right\} \cup \left\{H_a (t) \right\} \cup \left\{H_v (t) \right\} \cup \left\{H_c (t) \right\} }\right\vert$  \end{equation}  A well-studied feature of invasion by \textit{Salmonella} is the formation of epithelial cell membrane ruffles, triggered by effectors secreted via the bacterium's type III secretion system 1 (TTSS-1). We call the total number of ruffles $R (t)$, and the number of host cells with at least one ruffle $H_r (t)$.