A culture of bacteria have a growth rate (as a percent) given by [itex]kb[/itex] per year, constant [itex]k>0[/itex] and [itex]b[/itex] is the number of bacteria. A virus removes bacteria at a rate of [itex]m[/itex] bacteria per year. I am trying to model this information using an ODE, but might be making a mistake.
The Attempt at a Solution
If the percent growth rate is kb, [itex](dy/y)/dt = kb[/itex] so [itex]dy/dt = kb^2[/itex].
Add this to the removal rate, and [itex]dy/dt = kb^2 - m[/itex].
I am not sure the model is as simple as this, it would mean the units of k are [itex]1/(bacteria*year)[/itex], which sounds odd.