deletions | additions       diff --git a/section_Proofs_subsection_Bacterial_density__.tex b/section_Proofs_subsection_Bacterial_density__.tex  index 3d809da..e87df52 100644  --- a/section_Proofs_subsection_Bacterial_density__.tex  +++ b/section_Proofs_subsection_Bacterial_density__.tex 
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\dot{N}_r = \dot{r} N = (N - N_r) \Gamma_0 \rho_B f = (N - N_r) f \Gamma_0 \left(\frac{bmc}{a}\right)  \end{equation*}  \begin{equation*} \begin{equation}  \dot{r} = (1 - r) f \Gamma_0 \left(\frac{bmc}{a}\right)  \end{equation*} \end{equation}  \subsection*{Rate of bacteria capture} 
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=& - N \Gamma_0 \rho_B - N_R \Gamma_1 \rho_B = -N \rho_B (\Gamma_0 + \tilde{r} \Gamma_1)  \end{align}  \end{equation*}  \begin{equation}  \dot{b} = - \frac{bc}{a} (\Gamma_0 + \tilde{r} \Gamma_1)  \end{equation}