Heteroclinic Connection in a Nicholson's delayed model with Harvesting term

In this paper we prove the existence of monotone heteroclinic solutions for the delayed Nicholson’s blowflies model with harvesting: $$x^{\mathrm{\prime }}(t)=-\delta x(t)-Hx(t-\sigma )+\rho x(t-r)e^{-x(t-r)}\mathrm{.}$$ Under the condition $1<{\displaystyle \frac{\rho }{\delta +H}}\le e$, we establish the connection between the equilibria $0$ and $\ln (\rho \mathrm{/}(\delta +H))$ using the Wu and Zou monotone iteration method adapted for two delays ($\sigma \mathrm{\ne }r$). The proof combines explicit upper and lower solutions construction with characteristic equation analysis, supported by numerical simulations.