Your application looks impressive but you seem to reinvent some significant amount of wheel.

From what i see you directly include Sundails. Why did you decide not use the DiffEq universe and call Sundails without that?
If you did so you could try other algorithms which might lead to a faster/more precise solution.

There are some other packages in Julia which have significant overlap:
https://github.com/JuliaDiffEq/DiffEqParamEstim.jl and https://github.com/robertfeldt/BlackBoxOptim.jl
I am sure DiffEqParamEstim would be happy with such an well worked out and non-trivial example. Why did you decide to roll your own framework from scratch
? Do you see places where DiffEqParamEstim could improve to suit your needs?

BlackBoxOptim.jl might be interested in your evolutionary optimization algorithm, i think it already has some but having them behind the same calls would allow to compare those and pick a better one or improve the interface of BlackBoxOptim.jl.

Thank you for writing this package and welcome to the wider Julia community. I hope i did not bother you.