Attacks exploiting human attentional vulnerability have posed severe threats to cybersecurity. In this work, we identify and formally define a new type of proactive attentional attacks called Informational Denial-of-Service (IDoS) attacks that generate a large volume of feint attacks to overload human operators and hide real attacks among feints. We incorporate human factors (e.g., levels of expertise, stress, and efficiency) and empirical psychological results (e.g., the Yerkes-Dodson law and the sunk cost fallacy) to model the operators' attention dynamics and their decision-making processes along with the real-time alert monitoring and inspection. To assist human operators in dismissing the feints and escalating the real attacks timely and accurately, we develop a Resilient and Adaptive Data-driven alert and Attention Management Strategy (RADAMS) that de-emphasizes alerts selectively based on the abstracted category labels of the alerts. RADAMS uses reinforcement learning to achieve a customized and transferable design for various human operators and evolving IDoS attacks. The integrated modeling and theoretical analysis lead to the Product Principle of Attention (PPoA), fundamental limits, and the tradeoff among crucial human and economic factors. Experimental results corroborate that the proposed strategy outperforms the default strategy and can reduce the IDoS risk by as much as 20%. Besides, the strategy is resilient to large variations of costs, attack frequencies, and human attention capacities. We have recognized interesting phenomena such as attentional risk equivalency, attacker's dilemma, and the half-truth optimal attack strategy.