**5. Acknowledgment**

Part of this study was conducted as part of the collaborative research project between the Japan International Research Center for Agricultural Sciences (JIRCAS) and the Southern Horticultural Research Institute of Vietnam (SOFRI). In addition, part of this work was supported by KAKENHI (23780052). We thank Mr. Masato Shimajiri, Mr. Masakazu Hirata, and the staff of the Technical Support Section of TARF/JIRCAS for their help in managing and maintaining the experimental field for estimation of the parameters. We are grateful to Ms. Aya Yano, Mr. Kenji Mishima, Mr. Hiroyuki Murota, Ms. Kiyomi Toume and Satoshi Kawate for their help in producing the released insects and controlling our plant conditions for the parameter estimation.
