O.K., so I am a biologist that is better at math than most in my field and I've been tasked with a company to come up with a model for two insect species, call them P and L.

I have developed a modified Lotka-Volterra model with a delay differential equation for the predator population.

I just ran my stability analysis and found the non-trivial equilibrium to be (5.3,1.09).

Now, the model runs fine and dandy if I use relatively small numbers, but that isn't really helpful since we're talking about insect populations that should be in the thousands.

There is no oscillations if I use numbers whose size resembles that of insect populations.

I think this is a problem with one of the assumptions in Lotka-Volterra, which is that predators can consume infinite amounts of prey. For example my prey equation is as follows
DP/dt = .158P(1-P/2000) -.03PL where L is the predator population, .158 is the intrinsic growth rate of prey, 2000 is the carrying capacity, and .03 is the kill rate per interaction.

So, for large initial populations I have found that the term .03P*L becomes insanely large and just sinks the prey population to zero.

My question is with scaling. If I just say that the equilibrium is actually measured in the hundreds, or thousands of predator and prey respectively, will that really affect the nut and bolts of my model?

I have asked other biologists, but none of them know anything above Calculus I, so they are useless.

Any help would be appreciated.