**Core Concept**
The question describes a classic case of familial acne, a chronic inflammatory skin condition characterized by comedones, papules, nodules, and pustules, particularly on the face and upper back. The involvement of multiple family members at a similar age and the exacerbation of symptoms during a cruise to the Adriatic Sea, where the humidity and heat may have contributed to the worsening of the condition, point towards a bacterial etiology.

**Why the Correct Answer is Right**
The pathogenesis of acne involves a complex interplay between hormones, keratinization, and the bacterium *Propionibacterium acnes* (P. acnes). P. acnes is a gram-positive, anaerobic bacterium that is normally present on the skin in small numbers. However, in individuals with acne, the bacteria proliferate and contribute to the development of inflammatory lesions. The bacteria produce lipases that break down triglycerides in the sebum, leading to the formation of pro-inflammatory substances and the activation of the immune system. The exacerbation of symptoms during the cruise, where the humidity and heat may have increased the amount of sebum production, provides further evidence of the role of P. acnes in the pathogenesis of acne.

**Why Each Wrong Option is Incorrect**
* **Option B:** *Staphylococcus aureus* is a gram-positive bacterium that can cause a range of skin infections, including impetigo and folliculitis. However, it is not the primary bacterium involved in the pathogenesis of acne.
* **Option C:** *Malassezia* is a yeast that is normally present on the skin and can contribute to the development of conditions such as dandruff and seborrheic dermatitis. However, it is not directly involved in the pathogenesis of acne.
* **Option D:** *Demodex* is a genus of mites that can be found on the skin and may contribute to the development of conditions such as rosacea. However, it is not the primary bacterium involved in the pathogenesis of acne.

**Clinical Pearl / High-Yield Fact**
The use of topical retinoids, antibiotics, and benzoyl peroxide can help to reduce the severity of acne by decreasing the proliferation of P. acnes, preventing the formation of comedones, and reducing inflammation. Additionally, maintaining good skin hygiene, avoiding picking or squeezing lesions, and using sunscreen to prevent further inflammation can also help to manage acne.

**Correct Answer:** C. *Propionibacterium acnes* (P. acnes).