Hi, Today I am going to suggest "Blue Gender" an seinen post-apocalyptic science fiction anime where the world was overrun by giant insects.

Description:

Yuji, a high school teenager, discovers that he has an new incurable virus. With life looking very bleak, he's left only one option - hope that the future may hold a cure. With his decision made, he opts to undergo artificial hibernation...
When Yuji awakes, the world he knew is gone. The year is 2031 - an era of war, despair and death. While he's been sleeping, the Earth has been taken over by BLUE, a mysterious creature that eats anything for food including human beings.
Hunted and on the verge of extinction, Mankind has fled. Now, their only chance for survival is to destroy BLUE! Now, Yuji must fight not only for his own survival, but for that of the entire Human race!