You mention wanting a simple model that is easy to understand. Always a noble goal. You then relax your request to allow a complicated equation to model it.
@ruben3d suggests one fairly simple approach that can recover behavior to some extent. However one could argue that it does not 'model' anything.
I.e. the arbitrary functions drawn that happen to resemble the observed behavior do not have any explanatory value. You wanted something simple to understand -- @ruben3d's model does not advance understanding.
@ranier-p's approach uses a Newtonian flow model to explain behavior across a wide range of fully separated angle of attack. That does a lot to advance understanding.
For most aircraft use, we are most interested in the well behaved attached potential flow region (say +-8 deg or so). Much study and theory have gone into understanding what happens here. Another ASE question also asks for an equation for lift.
Is there a formula for calculating lift coefficient based on the NACA airfoil?
In this limited range, we can have complex equations (that lead to a simple linear model). These are based on formal derivations from the appropriate physics and math (thin airfoil theory). They are complicated and difficult to understand -- but if you eventually understand them, they have much more value than an arbitrary curve that happens to lie near some observations.
On the other hand, using computational fluid dynamics (CFD), engineers can model the entire curve with relatively good confidence.
From one perspective, CFD is very simple -- we solve the conservation of mass, momentum, and energy (along with an equation of state) for a control volume surrounding the airfoil. We divide that volume into many smaller volumes (or elements, or points) and then we solve the conservation equations on each tiny part -- until the whole thing converges. I.e. we subject the problem to a great deal computational brute force.
This is a very powerful technique capable of modeling very complex flows -- and the fundamental equations and approach are pretty simple -- but it doesn't always provide very satisfying understanding because we lose a lot of transparency in the computational brute force.
I.e. It could be argued that that the Navier Stokes equations are the simple equations that answer your question. But that probably isn't the answer you are looking for.
There is no simple answer to your question. Instead, there is the fascinating field of aerodynamics.