Contagious disease is spread by

The correct option is D Direct contact with an infected person
The diseases which are more infectious called as a contagious disease. It can be transmitted through direct contact with infected person. It is also called as a communicable disease.
Mosquitoes and other biting insects do spread diseases but not by mere contact. They need to insert their proboscis into the infected person to pick up and transmit the disease.
Contaminated food can cause the spread of disease but not by contagion. The food has to be ingested to cause the disease.
Thus, the correct answer is option D.