Every person in the State of Mississippi who owns, or has in his or her possession, any dog or cat of the age of three (3) months or over shall have said dog or cat inoculated (vaccinated) against rabies as provided herein with the recommended dosage of an anti-rabic virus (vaccine) approved by the State Board of Health, and it shall be unlawful for any person within the State of Mississippi to own or have in his or her possession within the State of Mississippi any dog or cat three (3) months of age or over which has not been inoculated (vaccinated) against rabies with the approved dosage of an approved anti-rabic virus (vaccine). It shall be the duty of every person in this state so owning or having in his or her possession a dog or cat to have said dog or cat inoculated (vaccinated) immediately after said dog or cat has reached the age of three (3) months, and it shall be said person's further duty to have said dog or cat so inoculated (vaccinated) thereafter as required by the State Board of Health. For a failure to comply with this section said person shall be subject to the penalties provided in Section 41-53-13.