The Soybean aphid (Aphis glycines) is a destructive pest that threatens soybeans. In order to develop green and effective control strategies, we propose an EQPAL epidemic model that integrates four developmental stages (1st–2nd stage nymphs, 3rd stage nymphs, 4th stage nymphs, and adults) and a ladybug (Harmonia axyridis) compartment. This model achieves green pest control by artificially releasing a natural enemy of soybean aphids to prey on adult soybean aphids. We analyzed the dynamic behavior of the model and derived the basic reproduction number ${\mathcal{R}}_0$. Using field monitoring data from Changchun City, Jilin Province, China in 2025, the segmented nonlinear least squares method was used for parameter estimation and fitting, resulting in an overall determination coefficient of $R^2=0.8204$. The numerical simulation results showed that the release of ladybugs significantly reduced the density and peak value of soybean aphid adults, and the predation rate $\beta$, predation conversion rate c, and ladybug migration rate $\omega$ were identified as key regulatory parameters. In addition, a cost–benefit analysis was conducted to determine the most cost-effective control measures.