The SARS-CoV-2 virus and COVID-19 disease have posed unprecedented and overwhelming demand, challenges and opportunities to domain, model and data driven modeling. This paper provides a comprehensive review of the challenges, tasks, methods, progress, gaps and opportunities in relation to modeling COVID-19 problems, data and objectives. It constructs a research landscape of COVID-19 modeling tasks and methods, and further categorizes, summarizes, compares and discusses the related methods and progress of modeling COVID-19 epidemic transmission processes and dynamics, case identification and tracing, infection diagnosis and medical treatments, non-pharmaceutical interventions and their effects, drug and vaccine development, psychological, economic and social influence and impact, and misinformation, etc. The modeling methods involve mathematical and statistical models, domain-driven modeling by epidemiological compartmental models, medical and biomedical analysis, AI and data science in particular shallow and deep machine learning, simulation modeling, social science methods, and hybrid modeling.
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