I came upon this alternative healing webpage. Interesting enough, there is a section there about what food should be eaten by a dengue patient. It did not state why specific foods are allowed or not. Anyway, it is always best to ask a doctor first.

Dengue patients� main meal should consist of rice gruel and boiled vegetables. Oil is a no-no and so are spices, including salt, although lemon juice may be used to flavor bland dishes. Porridge, baked toasts, or biscuits can be eaten for snacks throughout the day. Tea must be made of fever reducing herbs such as ginger and tulsi. The only fruits that can be eaten are apples and plaintain.

Source: The Ayushveda.com