have/having

Me neither. But you are right, I think.

If the verb in the first clause was "preventing" (present continuous?) then "having" would be the choice for the second clause.

Thanks, Mc Tag.

Your feeling is correct, but the sentences would benefit from rewriting.

Gerund

Most patients would prefer preventing infection to dealing with its results.

Infinitive

Most patients would rather prevent infection than deal with its results.

Old proverb: An ounce of prevention is worth a ton of cure.