Any person, whether a minor or adult, having been bitten or knocked down by an animal improperly or inadequately leashed or contained can sue for injuries or death caused by a bite or knock-down. You can sue the person who has or was responsible for the animal. For a person to be responsible they need not be the owner of the animal. However, an owner who maintains some control over the animal remains liable even if the animal is partly under the care of others.
You may be entitled to recover damages for past and future and medical expenses, past and future wage loss, past and future pain and suffering, and if it is deemed that conduct is severe enough, punitive damages (punishment damages against the defendant). If the victim dies, his or her survivors are entitled to recover full compensation for their financial losses that resulted from the victim's death, as well as emotional distress damages. If the survivors can prove that the victim lived for a period of time between the negligent act and death, they can also bring an action for punitive damages.
You can also sue if you were fleeing from an animal, and you reasonably feared for your safety and can prove that the owner or possessor of the dog knew or should have known of the dog's propensity to attack people walking nearby, and failed to act accordingly.
So if you own an animal with a propensity for biting strangers, make sure it is safely contained fenced, chained, boxed, whatever is necessary to protect you, your animal, and potential plaintiffs. If you are bitten by an animal and it creates a situation where a lawsuit is appropriate, be informed as to the criteria under which you can pursue and obtain damages.