Short Answer: Yes. An area spell is static in position unless otherwise specified.
From my experience working with the usage of spells in my campaigns, I find it safe to assume that, unless specified, an area spell cannot be moved by its caster's will. Many spells drop slight hints to this in their wording. Case in point being the spell in question.
In the case of Insect Plague, I would quote one part of the spell's text that alludes to it being a static area.
Insect Plague (5th level, Conjuration) The sphere remains for the duration, and its area is
Note the word "remains" in this context. If we just take that word into account, by its definition from the good ol' internet we get:
Verb : re·main
stay in the place that one has been occupying.
We can then assume that Insect Plague does indeed stay in the same spot, immobile.
Each spell that affects an area over a duration normally specifies whether it is mobile or not, Insect Plague was easily the least clear on that if you don't read into the text too much. Especially since it's a swarm of moving insects. Let's take Control Weather as a separate example for a moment.
Control Weather (8th level, Transmutation) You take control of the weather within 5 miles of you for the duration.
This spell also specifies where the area is, in this case Control Weather is movable, but only by moving yourself. The wording in spells can be finicky. So make sure you pay careful attention to how it describes the placement of the spell. When in doubt, refer to the PHB page 204 regarding spells for extra information regarding placement. It probably does a better job than I did.