Keep your pet indoors. If they do go outside, keep them on a leash. Have all pets surgically spayed or neutered. Neutered animals are less likely to roam and therefore less likely to contract diseases. Feed your pet only commercially prepared food and treats.
Animals can contract zoonotic infections from undercooked or raw meats or eggs.
Also, do not let your pet drink from the toilet because several zoonotic infections can be contracted by this route. Wash your hands after handling your pet, especially before you eat, prepare food, or smoke. Keep your cat's litter box away from eating areas. Use disposable pan liners so that the entire pan can be cleaned with each litter change. If possible, someone else should change the litter pan.