Try a polygon model of a revolution surface. The next example of that idea has low polygon count to keep the image sparse:
As a wireframe it's this:
It's turned to vertical position, the projection is parallel (=no perspective), the view was saved as PDF, opened in Illustrator and all horizontal and vertical lines are manually deleted:
This has nothing elegant, but at least it resembles the wanted pattern.
The revolution surface above was made in a CAD program. The revolved curve was originally a smooth spline. The surface was converted to STL-file with low resolution to get a polygon mesh.
ADD: There's a comment which suggests mapping a curve pattern along the surface. It needs much more advanced software than revolving a spline and converting the surface to a polygon mesh. I actually tried it in Illustrator with 3D revolve + art mapping, but the curves were expanded without asking to filled areas and became non-uniformly wide. The next method keeps the pattern as curves.
Making it as a 2D shape from scratch in Illustrator:
There's a rectangle and a diagonal line is drawn into it. The line is bent to approximate half-cycle sine curve. The node handles are stretched with the anchor type tool horizontally.
In the next image the sine curve is duplicated and both copies are moved to the corners of the rectangle:
The curves snap perfectly if you have smart guides and snap to point ON.
Make blend between the sine curves. I inserted 20 intermediate copies. The result is quite sparse, but easy to see:
Expand and Ungroup the blend to make the curves free. Select all and delete everything which is outside the rectangle with the shape builder tool (hold Alt for delete). It's done in the left in the next image:
In the right half all sine curves are selected and a flipped copy is made (=Object > Transform > reflect > Vertical > Copy). The rectangle is also colored to red.
Select all. Apply Object > Envelope distortion > Make with Mesh. Have 1 row and 2 columns in the mesh. Drag the mesh nodes and handles with the direct selection tool:
This IS tricky. It may be easier to envelope distort with Warp. Use preset "Bulge" with negative expansion. Adjust the mesh nodes and handles as needed.
You may want more room to adjust. More columns in the envelope distortion mesh give it, but things become very soon unmanageable because every mesh node has several handles which all should be right. One must draw some help lines to be able to adjust handles symmetrically in symmetric shape.
Expand the envelope distortion if you want the curves free for individual colors or other edits.