One of the central scientific goals of the next-generation Cherenkov Telescope Array (CTA) is the detection and characterization of gamma-ray bursts (GRBs). CTA will be sensitive to gamma rays with energies from about 20 GeV, up to a few hundred TeV. The energy range below 1 TeV is particularly important for GRBs. CTA will allow exploration of this regime with a ground-based gamma-ray facility with unprecedented sensitivity. As such, it will be able to probe radiation and particle acceleration mechanisms at work in GRBs. In this contribution, we describe POSyTIVE, the POpulation Synthesis Theory Integrated project for very high-energy emission. The purpose of the project is to make realistic predictions for the detection rates of GRBs with CTA, to enable studies of individual simulated GRBs, and to perform preparatory studies for time-resolved spectral analyses. The mock GRB population used by POSyTIVE is calibrated using the entire 40-year dataset of multi-wavelength GRB observations. As part of this project we explore theoretical models for prompt and afterglow emission of long and short GRBs, and predict the expected radiative output. Subsequent analyses are performed in order to simulate the observations with CTA, using the publicly available ctools and Gammapy frameworks. We present preliminary results of the design and implementation of this project.
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