(a) All expenses legally incurred for the work of protecting the public health outside of cities and towns shall be paid by the county in which the expense is incurred, and claims shall be allowed by the county court when proved as other claims against a county are required by law to be proved; however, every claim must be approved by the county health officer before allowance.
(b) The expense legally incurred for the protection of public health inside corporate limits of cities and towns shall be paid out of the treasury of the cities and towns in which the work is done.
(c) All of the expenditures made by representatives of the State Board of Health and chargeable, under the provisions of this act, to any county, city, or town shall be made only with the advice and consent of the county judge of the county, or of the city board of health in any city of the first or second class, or of the mayor and town council in any incorporated town.
(d) From the judgment of the county court upon a claim, the claimant or any taxpayer of the county may appeal to the circuit court and thence to the Supreme Court.