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This paper is concerned with the existence of traveling wave solutions in delayed reaction diffusion systems which at least contain multi-species competition, cooperation and predator-prey models with diffusion and delays. By introducing the mixed quasimonotone condition and the exponentially mixed quasimonotone condition, we reduce the existence of traveling wave solutions to the existence of a pair of admissible upper-lower solutions. To illustrate our main results, the existence of traveling wave solutions of multi-species competition, cooperation and predator-prey Lotka-Volterra systems with delays is considered. In particular, we show the precisely asymptotic behavior of the traveling wave solutions of these Lotka-Volterra systems.2000 Mathematics Subject Classification. Primary: 35K57, 92D25; Secondary: 34C37, 34K10.

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Purpose Few features characterizing the dosimetric properties of the patients are included in currently available dose‐volume histogram (DVH) prediction models, making it intractable to build a correlative relationship between the input and output parameters. Here, we use planning target volume (PTV)‐only treatment plans of the patients (i.e., the achievable dose distribution in the absence of organs‐at‐risk (OAR) constraints) to estimate the potentially achievable quality of treatment plans and establish a machine learning‐based DVH prediction framework with the use of the dosimetric metric as model input parameters. Methods A support vector regression (SVR) approach was used as the backbone of our machine learning model. A database containing volumetric modulated arc therapy (VMAT) plans of 63 prostate cancer patients were used. For each patient, the PTV‐only plan was generated first. A correlative relationship between the OAR DVH of the PTV‐only plan (model input) and the corresponding DVH of the clinical treatment plan (CTP) (model output) was then established with the 53 training cases. The prediction model was tested by the validation cohort of ten cases. Results For the training cohort, the checks of dosimetric endpoints (DEs) indicated that 52 of 53 plans (98%) were within the 10% error bound for bladder, and 45 of 53 plans (85%) were within the 10% error bound for rectum. In the validation tests, 92% and 96% of the DEs were within the 10% error bounds for bladder and rectum, respectively, and eight of ten validation plans (80%) were within the 10% error bound for both the bladder and rectum. The sum of absolute residuals (SAR) achieved a mean of 0.034 ± 0.028 and 0.046 ± 0.021 for the bladder and rectum, respectively. Conclusions A novel dosimetric features‐driven machine learning model with the use of PTV‐only plan has been established for DVH prediction. The framework is capable of efficiently generating best achievable DVHs for VMAT planning.