COVID-19 pandemic has caused unprecedented negative impacts on our society, including further exposing inequity and disparity in public health. To study the impact of socioeconomic factors on COVID transmission, we first propose a spatial-temporal model to examine the socioeconomic heterogeneity and spatial correlation of COVID-19 transmission at the community level. Second, to assess the individual risk of severe COVID-19 outcomes after a positive diagnosis, we propose a dynamic, varying-coefficient model that integrates individual-level risk factors from electronic health records (EHRs) with community-level risk factors. The underlying neighborhood prevalence of infections (both symptomatic and pre-symptomatic) predicted from the previous spatial-temporal model is included in the individual risk assessment so as to better capture the background risk of virus exposure for each individual. We design a weighting scheme to mitigate multiple selection biases inherited in EHRs of COVID patients. We analyze COVID transmission data in New York City (NYC, the epicenter of the first surge in the United States) and EHRs from NYC hospitals, where time-varying effects of community risk factors and significant interactions between individual- and community-level risk factors are detected. By examining the socioeconomic disparity of infection risks and interaction among the risk factors, our methods can assist public health decision-making and facilitate better clinical management of COVID patients.