This insect transmits relapsing fever

The correct option is Cimex.

Relapsing fever is a bacterial infection characterized by recurring episodes of fever, headache, muscle and joint aches, and nausea. It is caused by certain species of spirochetes of the genus Borrelia.
This infection is transmitted to humans through the bites of infected arthropods. Depending on the vector, it is classified into two main types: louse-borne relapsing fever (LBRF) and tick-borne relapsing fever (TBRF).

Cimex lectularius (commonly known as the bedbug) belongs to the genus Cimex. While body lice (Pediculus humanus humanus) are the primary vector for epidemic louse-borne relapsing fever, bedbugs (Cimex) have historically been associated with the transmission of various pathogens, including the spirochetes responsible for relapsing fever in certain environments, making it the correct match among the choices provided.

Let's look at why the other options are incorrect:
- Apis: This is the genus of honeybees, which are known for producing honey and pollinating plants, not for transmitting infectious diseases like relapsing fever.
- Drosophila: This is the genus of small fruit flies, commonly used as model organisms in developmental biology and genetics, and they do not vector relapsing fever.
- Gryllus: This is the genus of field crickets, which are harmless to humans regarding disease transmission.