Sadasivan et al.write [1]:

"Influenza A viruses infect a number of different species, ranging from birds to mammals including humans... In addition to the well-defined respiratory effects, acute influenza infection in humans can lead to the development of a number of encephalitic syndromes, each having neurological consequences... We demonstrated that acute infection in mice with two different influenza viruses, A/Vietnam/1203/2004 (highly pathogenic avian H5N1 virus)... and A/California/04/2009 H1N1 virus,.. induces an inflammatory response in the brain, consisting of activation of microglia and secretion of cytokines/chemokines... This suggested that the peripheral immune response activated following influenza infection ... was likely responsible for the observed secondary Central Nervous System (CNS) inflammation."

They point out that flu jabs and anti-virals may help reduce the likelihood of PD developing.

Reference

[1] "Synergistic effects of influenza and 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) can be eliminated by the use of influenza therapeutics: experimental evidence for the multi-hit hypothesis"
Shankar Sadasivan, Bridgett Sharp, Stacey Schultz-Cherry & Richard Jay Smeyne
npj, May 2017
Synergistic effects of influenza and 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) can be eliminated by the use of influenza therapeutics: experimental evidence for the multi-hit hypothesis | npj Parkinson'''s Disease

John