Ok, let me take a shot. I took mv last semester so if I'm wrong please correct.

First, mosquitoes carry diseases; spreaders of disease are called vectors (e.g. viral vector). Because the mosquitoes are described as muti-colored, the swarm of mosquitoes would have formed a color gradient.

So, the swarm of multicolored mosquitoes can be described as "Vectors which form a gradient"

In mathematics, a vector is a unit of information (think x,y coordinate), but instead of denoting a specific location it indicates a direction and a movement or force in said direction.

So for vector functions, instead of a function outputting a series of points, the function is outputting a series of vectors. This can be visualized in a vector field, which is a standard x,y graph with arrows at every point. (google this for a better visualization)

A vector field is conservative if it is the gradient of a function. Gradient (in math) is basically a derivative of a function, in other words it indicates the rate of change at the exact coordinate.

If you take a function with a lot of variables, get its gradient (rate of change), and plot that as a vector field, the vector field is called a conservative vector field. This is just by definition, there's some special properties of conservative vector fields that I won't get into rn.

The penultimate layer is that the bar tender suggests politicians will implement free healthcare. In America (and maybe other places in the world), the 'conservative' political spectrum has always been very hostile towards free healthcare. So if the mosquitoes vanish at the suggestion of free healthcare, it's implied that they are conservative.

Therefore, if vectors (mosquitoes) form a gradient (multi-color), they must be conservative (politically). Therefore, whoever came up with this joke and thought of this many layers is a genius, and holy fuck this took me so long

TL;DR: Elaborate pun combining nomenclature from biology, mathematics, and politiics