Currently, dxDateBox does not provide API that allows you to disable specific dates: T260958: dxDateBox - Is it possible to disable dates?. However, it is possible to implement a workaround. The main idea is to select elements with necessary content by using jQuery and disable them. To get the information about a particular calendar cell, use the "aria-label" attribute (this is the most convenient way to determine the day of the week for a particular cell) or any other HTML attribute that meets your requirements (for instance, "data-value").
To determine the appropriate attribute, inspect the elements in the calendar like it is described in the K18570: How to inspect CSS rules article.