The variations of SIkJalpha model for COVID-19 forecasting and scenario projections

We proposed the SIkJalpha model at the beginning of the COVID-19 pandemic (early 2020). Since then, as the pandemic evolved, more complexities were added to capture crucial factors and variables that can assist with projecting desired future scenarios. Throughout the pandemic, multi-model collaborative efforts have been organized to predict short-term outcomes (cases, deaths, and hospitalizations) of COVID-19 and long-term scenario projections. We have been participating in five such efforts. This paper presents the evolution of the SIkJalpha model and its many versions that have been used to submit to these collaborative efforts since the beginning of the pandemic. Specifically, we show that the SIkJalpha model is an approximation of a class of epidemiological models. We demonstrate how the model can be used to incorporate various complexities, including under-reporting, multiple variants, waning of immunity, and contact rates, and to generate probabilistic outputs.