Final answer:
Neurological diseases that cause facial weakness or paralysis can range from Bell's palsy to myasthenia gravis or amyotrophic lateral sclerosis (ALS), which all require professional medical evaluation and testing.
Step-by-step explanation:
A neurological disease that causes weakness or paralysis on one side of the face can be a condition like Bell's palsy, where there is a sudden onset of muscle weakness on one side of the face due to nerve malfunction. However, in the context provided, and especially with symptoms like hemiparesis and a stiff neck, it could be a severe infection, or a central nervous system disorder that might be causing these neurological deficits. Conditions such as myasthenia gravis, which is an autoimmune disorder, can cause muscle weakness, especially starting around the eyes. Another serious condition is amyotrophic lateral sclerosis (ALS), which leads to the degeneration of motor neurons controlling voluntary muscles, progressing to paralysis over time. It’s important to undergo medical evaluation and testing to determine the exact cause of such neurological symptoms as these.