Dribbling of saliva is a common problem in Parkinson's disease.
There are a number of steps that you can take for this.
The first thing is to ask for a referral to a speech therapist, they can determine whether you have a swallowing problem.
There are also a number of medicines that your doctor can prescribe for you:
Anti cholinergic drugs - this can reduce the saliva produced by your salivary glands.
Scopalamine patch - this also works by reducing saliva production
Eye atropine drops - this can be used sublingually to decrease saliva production
Botulinum toxin - botox injections can also be used for this.
Discuss allt his with your doctor, your doctor can solve your problem with these steps.
Meanwhile some steps that you can start on your own from now are:
Such at hard candy - this will promote swallowing and keep your throat moist.
Wear a sweat band on your wrist - you can use this to wipe off saliva discreetly.
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Thank you and I wish you the best of health - stay safe!
Dr. P. Jyoti