Team:British Columbia/Modeling

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Reaction Kinetics: - Modelling the production of cinnamaldehyde, vanillin and caffeine production

Population dynamics: - Modelling the population of a bacteria in a batch reactor with phage dependency

\begin{align} \frac{dX}{dt} = \frac{dX_u}{dt} + \frac{dX_i}{dt} + \Gamma \end{align} Where $\frac{dX}{dt}$ is rate of change in bacteria population over time, $\frac{dX_u}{dt}$ and $\frac{dX_i}{dt}$ are the rates of change in the uninfected and infected populations respectively. $\Gamma$ is defined as a stepwise function. \begin{align} \Gamma &= - E(X_i), \ during \ phage \ caused \ lysis\\ &= 0, \ \ \ \ \ \ \ \ \ \ \ \ \ \ otherwise \end{align} Where $E(X_i)$ is the statistically expected infected bacterial populations. We define the rate of change in population in () and (). \begin{align} \frac{dX_u}{dt} = \mu_u + k_d \end{align}