Evening All, Im new to the forum so apologies if I dont give enough detail to be clear to start with.

Basically I have a fairly simple set of differential equations that are modelling the competition relation between a bacteria and healthy cells in a wound. The equations given are as follows:

dX/dt = rX(1-X/K) - aXY/(b+X)

dY/dt = sY(1-Y/C) - dXY

where r,s,K,C,a,b,d are non-negative constants. X represents skin cells and Y represents bacteria

My task is to add one additional ODE and modify the given equations to model the introduction of a drug (Drug Z). It must then describe the effect of this drug based on the following:

If a wound heals, the drug has no effect on the final healthy skin density

The growth rate of skin cells increases with Z to a maximal bounded level

Bacteria death rate increases with Z and is not limited in Z

Z is consumed by both skin cells and bacteria

My instinct would be to model the increase in the growth rate of skin cells logistically as it needs to be bounded. I assume bullet point 2 is suggesting that there needs to be a Y component in this part of the modification too, so that when Y is not present, no increase is seen (i.e. BP 1)

Also, for the additional equation I would assume it would just be a simple proportional decay of Z based on X and Y but not sure if there would need to be a growth term for Z too.

Any help is very much appreciated and if I haven't made myself clear please shout.

Thanks!