The invention provides methods to inhibit the replication of a flavivirus, methods of inhibiting the guanosine triphosphate (GTP)-binding and guanylyltransferase activity of a flavivirus RNA capping enzyme, and methods of treating a subject infected with a flavivirus. The methods can include contacting a flavivirus with an effective amount of a thioxothiazolidine compound described herein, or a derivative thereof, such as a compound of Formula (I).