Welcome to 2CarPros. That appears to be one of the PCV (Positive Crankcase Ventilation) hoses. I wouldn't drive it a lot with that open. It will allow dust and grime into the engine.
It is just common hose so shouldn't be hard to replace with a section off the parts shelf.
I would also look at all the other wires and hoses for damage, very likely there is other damage. Rodents are a real bother. Honda sells an anti-rodent tape that has pepper extract in it that helps keep them from eating the wires and such, not cheap but it's another tool.
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Monday, September 30th, 2019 AT 6:45 AM