The correct answer is option 3: Both 1 and 2.

Statement 1: In tropical regions, Zika virus disease is transmitted by the same mosquito that transmits dengue.

This statement is correct. The mosquito species Aedes aegypti and Aedes albopictus are the primary vectors responsible for the transmission of Zika virus disease in tropical regions. These same mosquito species are also responsible for the transmission of dengue, chikungunya, and yellow fever. Aedes aegypti is the main vector responsible for transmitting Zika virus disease, but Aedes albopictus can also transmit the virus.

Statement 2: Sexual transmission of Zika virus disease is possible.

This statement is also correct. Zika virus can be transmitted through sexual contact, including vaginal, anal, and oral sex, from a person who is infected with Zika virus to their sexual partner. The virus can also be transmitted from a pregnant woman to her fetus, which can cause congenital Zika syndrome, a severe neurological disorder.

Zika virus can also be transmitted through blood transfusion, although this is a rare occurrence. Moreover, the virus can be transmitted through the bite of infected mosquitoes, which is the primary mode of transmission.

In conclusion, both statements are correct, and option 3 is the correct answer.