I have a Maltipoo and yorkie puppies.?

I'm sorry what?

Have you taken them to the vet to get their shots?
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If they have worms get them dewormed and then you never have to ask this question.
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No, unless they eat there poop then yes. They are transmitted via a fecal oral route and you need to take your puppies to the vet to get started with proper care and deworming
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as long as your dogs are up to date with their womers you will be fine, but dogs mouths are very clean as their bacteria in their mouths destorys any germs.

I read recently that a dog that licked a plate got it cleaner and with less germs on than one that was washed in a dishwaser.

x
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There is NO such thing as a Maltipoo - what you have is a Maltese/Poodle cross.
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no you wont get worms unless they have ring worm you can catch that.
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