Is Herpes Simplex Virus Transmission Possible Through Inanimate Objects?

If i have herpes simplex on my lip but it goes away, can i reinfect myself ~ a week later via my toothbrush? I was under the impression that you cant reactivate the virus via contact with the virus once you have it. In a more basic way, if i already have the herpes virus, can contact with the virus cause mine to flare up? Additionally, can you auto-inoculate yourself in other parts of your body?