Can I nondimensionalize the model only when the total population is constant?

Question

I have the following ODE model that I nondimensionalized and I received feedback on it saying that "Author scale the population of human by divide each class with the total of human population (N_h). Author can do this only if the total of human population is constant. As equation (10) shows, there exist a death rate due to diseases in their model. Hence, all calculation which use a scale of the human population should be recalculated." I am wondering if the reviewer wants me to not do nondimensionalization and use equations 1-9 to do further analysis instead of using equations 15-19. Any help would be appreciated.

Answer 1

Yes, that is a grave error. You either use constants in the non-dimensionalisation, which means that $N_h$ and $N_v$ reduce to non-constant dependent variables $n_h$ and $n_v$. Or you need to apply the quotient rule $$ \frac{d}{dt}\frac{X}{N}=\frac{\dot X}{N}-\frac{\dot N}{N}·\frac{X}{N}, $$ You can not leave out the second term, you would get a different dynamic.