Here I enclosed the map from a part of The Persian Gulf.
I draw the map with ggmap function. Now I want to draw spatial analysis by kriging method or Gaussian process regression. My data frame consist of 3 vector. longitude, latitude and density.
My main question is how I can draw spatial analysis result over this map?
Note that the illustration in the paper you have attached used an extra-/interpolation technique to estimate the density in space. Not sure if your question is on how to do that, or how to customize the colours in the example that I've provided. The latter can be easily achieved as shown in the attached example.
If you want to produce illustrations similar to that you have attached, you could have a look at kriging techniques (see for instance the kriging-package). This will allow you to interpolate spatial point measurements taking into account spatial auto-correlation in your data...