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\subsection{Counts}  During the time course of  invasion process, by \textit{Salmonella},  a bacterium caneither  be in 4 different generalized stages: swimming (looking to attach to a host) $B$,  attached to a host cell $B_a$, invaded a host cell $B_x$, and vacuolar $B_v$,  or neither (i.e. swimming around looking to attach) $B_u$. These invaded and cytosolic $B_c$. The counts of bacteria in these stages  are mutually exclusive, so constantly changing in time, but ignoring xenophagy and replication,  the total number of bacteria is $B_{\rm will remain constant:    $B_[\rm  tot} = B_a B(t)  + B_x B_a(t)  + B_u$. This is, of course, ignoring bacterial replication and xenophagy. B_x(t) + B_c(t)$  We classify the relationship between host cells and bacteria in one of three ways: host cells with no bacteria $H_u$, $H$,  with attached bacteria $H_a$ $H_a$, with invaded vacuolar bacteria $H_v$,  and with invaded cytosolic  bacteria $H_x$. $H_c$.  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 union of these sets:  %$H_{\rm tot} = \left\vert{ \left{H \right}(t) \cup \left{H_a \right}(t) \cup \left{H_v \right}(t) \cup \left{H_c \right}(t) }\right\vert $  both internal (invaded) and external (attached) bacteria so we define another parameter $H$ which is simply the number of host cells with one or both. The total number of host cells is therefore $H_{\rm tot} = H + H_u$. An important and controllable quantity when performing invasion assays is the ratio of bacteria to host cells at inoculation. This is called the multiplicity of infection (MOI) and in terms of previously defined parameters, $m = B_{\rm tot} / H_{\rm tot}$.