  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.
