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

For the Nicholson’s blowflies equation with delayed mortality N ′ ( t ) = m ( t ) − δ N ( h 1 ( t ) ) + P N ( h 2 ( t ) ) e − γ N ( h 2 ( t ) ) , P > δ , 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.