Nicholson’s blowflies differential equations with a small delay in the mortality term

For the Nicholson’s blowflies equation with delayed mortality $N^{\prime }\left(t\right)=m\left(t\right)\left(-\delta N\left(h_1\left(t\right)\right)+PN\left(h_2\left(t\right)\right)e^{-\gamma N\left(h_2\left(t\right)\right)}\right),P>\delta ,$positivity, persistence, and boundedness of solutions are established. Two global stability tests for the positive equilibrium are obtained based on a linearized global stability method, reducing stability of a non-linear model to a specially constructed linear equation. The first one extends the absolute stability result to the case of delayed mortality and the second test is delay-dependent.