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- #1

$$

\frac{dN}{dt} = N(a-bP)\quad\text{and}\quad\frac{dP}{dt} = P(cN-d)

$$

How can this model be modified to demonstrate farmers who continual spray insecticides that kill both predator and prey (the predators and prey are insects)?

$$

\frac{dN}{dt} = N(a-bP) - \gamma\quad\text{and}\quad\frac{dP}{dt} = P(cN-d)-\rho

$$

Where $\gamma$ and $\rho$ are the insecticide deaths. Could $\gamma=\rho$? Or would it affect them different?

I just made up gamma and rho as the variables for the deaths. I am not sure if they would kill equally the predator and prey or the same.