Step 1: Understanding the Question:
The question asks to identify the specific mosquito genus that acts as the biological vector for transmitting the parasites responsible for filariasis.
Step 2: Detailed Explanation:
Filariasis, specifically lymphatic filariasis (elephantiasis), is caused by filarial worms like Wuchereria bancrofti.
These parasites require an intermediate host (vector) to spread from one human to another.
The Culex mosquito (particularly Culex quinquefasciatus) is the primary vector for this disease in many regions.
When an infected mosquito bites a human, the third-stage filarial larvae are deposited on the skin and enter the body through the bite wound.
Step 3: Final Answer:
Therefore, the disease is transmitted by the Culex mosquito.