There was an article last year that pointed to possible viral origins of neurodegenerative diseases in general: Can the Flu and Other Viruses Cause Neurodegeneration?
A neurobiologist saw a duck acting strangely in a video, as if it had Parkinson's disease. In an experiment he then ran, he infected ducks with H5N1 and found that the virus had induced degeneration in the ducks' brains: inflammation and cell death.
It's hypothesised that influenza viruses can cause the same thing in humans. A literature review revealed a secondary outbreak of Parkinson's disease happening in 1940-1950, following the 1918-1919 H1N1 influenza pandemic.
As for the current pandemic, SARS-CoV-2, the virus that causes COVID-19, can infect the central nervous system, breach the blood-brain barrier and enter the brain. It can cause symptoms like failure to breathe spontaneously, as well as the anosmia (lack of sense of taste or smell) that has been seen in the absence of blocked sinuses.
So, COVID-19 could cause similar neurodegeneration in some time.