Mean Field Model of Infection



\(N\equiv\) number of host cells

\(N_{I}\equiv\) number of infected cells

\(N_{B}\equiv\) number of bacteria

\(N_{R}\equiv\) number of ruffles

\(N_{r}\equiv\) number or ruffling cells (\(\geq 1\) ruffles)

\(t_{\mathrm{max}}\equiv\) total incubation time


\(m\equiv\) multiplicity of infection (MOI) \(=\frac{N_{B}(t=0)}{N}\)

\(c\equiv\) confluency \(=\frac{Na}{L^{2}}\)

\(\quad a\equiv\) mean cellular area

\(\quad L\equiv\) side length of square well

\(x\equiv\) fraction of host cells infected \(=\frac{N_{I}}{N}\)

\(b\equiv\) fraction of bacteria remaining (i.e. not landed on a host) \(=\frac{N_{B}}{N_{B}(0)}\)

\(f\equiv\) fraction of attached bacteria that form ruffles

\(r\equiv\) fraction of host cells with ruffling (\(\geq\) 1 ruffle)

\(\tilde{r}\equiv\) ruffles per cell \(=\frac{N_{R}}{N}\)

\(\tilde{b}_{R}\equiv\) bacteria per ruffle



\(\Gamma_{0}\equiv\) primary attachment rate per bacterial density

\(\Gamma_{1}\equiv\) ruffle recruitment rate per bacterial density