Abstract
The COVID-19 pandemic has significantly challenged traditional epidemiological models due to factors such as delayed diagnosis, asymptomatic transmission, isolation-induced contact changes, and underreported mortality. In response to these complexities, this paper introduces a novel CURNDS model prioritizing compartments and transmissions based on contact levels, rather than merely on symptomatic severity or hospitalization status. The framework surpasses conventional uniform mixing and static rate assumptions by incorporating adaptive power laws, dynamic transmission rates, and spline-based smoothing techniques. The CURNDS model provides accurate estimates of undetected infections and undocumented deaths from COVID-19 data, uncovering the pandemic's true impact. Our analysis challenges the assumption of homogeneous mixing between infected and non-infected individuals in traditional epidemiological models. By capturing the nuanced transmission dynamics of infection and confirmation, our model offers new insights into the spread of different COVID-19 strains. Overall, CURNDS provides a robust framework for understanding the complex transmission patterns of highly contagious, quarantinable diseases.