Herpes Simplex Virus (HSV) Infection: Despite the negative HSV DNA swab, the recurrent nature of the lesion and its description as a circular erosion are highly suggestive of HSV. The swab may have been collected too late after the onset of symptoms to detect the virus, as viral shedding decreases over time.

Syphilitic Chancre: The lesion's appearance and location near the anus could be consistent with primary syphilis, especially if the patient has been sexually active. However, the recurrent nature is less typical for syphilis.
Anal Fissure: While not typically described as a circular erosion, an anal fissure could present with a small, painful lesion near the anus. The recurrent nature might be explained by repeated trauma or irritation.
Molluscum Contagiosum: This viral infection can cause small, circular lesions, but they are usually multiple and can be found in various locations, not just near the anus.

Squamous Cell Carcinoma or Other Malignancies: Although rare, any persistent or recurrent lesion near the anus should prompt consideration of malignancy, especially in immunocompromised patients or those with a history of high-risk HPV or HIV.
Lymphogranuloma Venereum (LGV): This sexually transmitted infection can cause lesions, though they are more commonly found on the genitals. The possibility of LGV, especially in someone with multiple sexual partners, should not be overlooked due to its potential for serious complications.

Behçet's Disease: This condition can cause genital ulcers, among other symptoms, but it is rare and typically involves other systemic manifestations.
Granuloma Inguinale (Donovanosis): A bacterial infection that can cause genital ulcers, but it is uncommon in many parts of the world and typically presents with beefy-red ulcers rather than small, circular erosions.