We present a physical model for recently demonstrated high indium content self-assembled In0.4Ga0.6N/GaN quantum dot (QD)-based ridge-waveguide lasers emitting at red wavelengths. The strain distribution in the QD is calculated using linear elastic theory with the application of shrink-fit boundary condition at the InGaN/GaN material interface, and the electronic states are evaluated using a single-band effective mass Hamiltonian. A Schrödinger-Poisson self-consistent solver is used to describe the effect of charge screening under current injection. Our theoretical result shows a good match to the measured Hakki-Paoli gain spectrum. Combining the calculated gain spectrum and cavity properties, we have developed a device-level simulation to successfully explain the electrical and optical characteristics of this specific laser. Possible solutions to improving the device performance have been explored.