Final answer:
The veins involved in the transmission of infection in the patient's condition likely include the facial vein, superior and inferior ophthalmic veins, and potentially the deep facial vein, depending on the specific location of the infection.
Step-by-step explanation:
The veins that could have been involved in the transmission of infection in a patient with a condition affecting the facial area would likely be those in close anatomical proximity to the infection site. Considering the anatomical structures of the head and neck, the vessels likely involved in such an infection could include the facial vein which drains blood from the facial region, the superior ophthalmic vein which is involved in the venous drainage of the eyes and part of the orbit, and the inferior ophthalmic vein, which similarly drains the orbit. The deep facial vein could also be involved due to its connections with the facial vein and the pterygoid plexus.
The inferior alveolar vein, which typically drains the lower jaw, may be less likely to be involved unless the infection is situated near the lower mandibular region. It is important to note that infections in venous systems can quickly spread due to the venous connections and may lead to serious complications like septicemia or thrombophlebitis.