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We propose a novel non-excitonic computationally efficient numerical model based on rate equations to describe the spectral characteristics of quantum-dot (QD) super-luminescent diodes (SLDs). It takes into account the inhomogeneous gain broadening due to dot-size dispersion, the effect of QD layers emitting at different wavelengths, and the nonuniform longitudinal distribution of gain and optical power along the waveguide. The model is applied to evaluate the effectiveness of chirping the QD layers in improving the SLD spectral bandwidth and output power. Simulated and experimental results are in good agreement in terms of output power and spectral characteristics versus current. Finally, an example of the possibility to apply the model to optimize SLD performances in terms of spectral bandwidth and power is shown.