Which condition is indicated by an erythematous rash on the cheeks and bridge of the nose accompanied by fatigue?

The presence of an erythematous rash on the cheeks and the bridge of the nose, coupled with fatigue, is characteristic of lupus erythematosus, particularly systemic lupus erythematosus (SLE). This condition often presents with a distinctive "butterfly" rash, which appears on the face in a symmetrical pattern across the cheeks and nose. The fatigue associated with lupus is due to various factors, including autoimmune processes, chronic inflammation, and anemia, which are common in this condition.

In contrast, while atopic dermatitis can cause facial rashes, it typically appears as dry, itchy patches rather than the specific erythematous butterfly formation seen in lupus. Thyroid disease can lead to fatigue and skin changes but does not specifically manifest as a facial rash in this characteristic pattern. Rosacea, although it can cause facial erythema, usually does not present with significant fatigue and tends to involve flushing and acne-like breakouts, rather than the classic systemic symptoms associated with lupus. Thus, lupus erythematosus aligns closely with the symptoms described in the question.