We propose a new functional additive hazards model to investigate potential effects of functional and scalar predictors on mortality risks, and develop a penalized least squares estimation approach for model parameters.  The consistency, the convergence rate and the joint asymptotic distribution of the resulting estimator are established. A new finding is that the proposed estimators of scalar and functional coefficients are dependent asymptotically in the framework of the functional additive hazard model, while the scalar and functional estimators under the functional Cox model are independent asymptotically. Our simulation studies demonstrate that the proposed estimation procedure performs well. For illustration, we apply the proposed method to the COVID-19 data that motivated this research. The analysis results provide evidence to support the claim that minimizing community interactions indeed reduces mortality risks induced by COVID-19.