**Core Concept**
The question is testing the diagnosis of a specific skin condition characterized by itchy papular lesions, particularly in a genetic or familial pattern. The condition is caused by an allergic reaction to a specific antigen, leading to a type IV hypersensitivity reaction.

**Why the Correct Answer is Right**
The correct answer is an example of an allergic contact dermatitis, specifically caused by scabies mites. The scabies mites (Sarcoptes scabiei) burrow into the skin, causing a type IV hypersensitivity reaction, leading to the characteristic itchy papular lesions. The condition is highly contagious and can be spread through close contact with an infected person. The lesions are typically found in interdigital spaces, wrists, and genital areas, as seen in the child and his younger brother.

**Why Each Wrong Option is Incorrect**
* **Option A:** This is incorrect because scabies is not caused by a bacterial infection, but rather by a parasitic infestation.
* **Option B:** This is incorrect because impetigo is a bacterial skin infection characterized by honey-colored crusts and is not typically itchy or papular.
* **Option C:** This is incorrect because atopic dermatitis is an allergic condition, but it typically presents with dry, scaly, and lichenified skin, rather than itchy papular lesions.

**Clinical Pearl / High-Yield Fact**
The "burrow sign" is a classic clinical finding in scabies, where a small, thread-like burrow is visible on the skin surface, especially in areas like the webs of fingers and toes.

**Correct Answer: D. Scabies**