I had originally planned on producing a worldwide human density map, but the graphics available don't allow for setting the color of each country. So, I built a density map for the United States.

The algorithm is:

1. Obtain graphic shapes for each of the states.
2. Obtain the density for each state.
3. Decide on a color range and apply the lowest density to one end of the range and the highest to the other end.
4. For each state:
   
   • Determine it's density
   • Lookup that density value in the range and select a color
   • Draw the state

This is coded with the following (comments embedded as the code proceeds):

%matplotlib inline
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
from matplotlib.patches import Polygon
import pandas as pd
import numpy as np
import matplotlib
# create the map
map = Basemap(llcrnrlon=-119,llcrnrlat=22,urcrnrlon=-64,urcrnrlat=49,
        projection='lcc',lat_1=33,lat_2=45,lon_0=-95)
# load the shapefile, use the name 'states'
# download from https://github.com/matplotlib/basemap/tree/master/examples/st99_d00.dbf,shx,shp
map.readshapefile('st99_d00', name='states', drawbounds=True)
# collect the state names from the shapefile attributes so we can
# look up the shape obect for a state by it's name
state_names = []
for shape_dict in map.states_info:
    state_names.append(shape_dict['NAME'])
ax = plt.gca() # get current axes instance
# load density data drawn from
# https://en.wikipedia.org/wiki/List_of_U.S._states_by_population_density
df = pd.read_csv('states.csv')
print(df.head())
State        rank density/mi2  density/km2  pop_rank   2015_pop
New Jersey      1       1,218          470        11  8,958,013  
Rhode Island    2       1,021          394        43  1,056,298  
Massachusetts   3         871          336        15  6,794,422  
Connecticut     4         741          286        29  3,590,886  
Maryland        5         618          238        19  6,006,401  
   land_rank area_mi2   area_km2 
0         46    7,354  19,046.80 
1         50    1,034   2,678.00 
2         45    7,800  20,201.90 
3         48    4,842  12,540.70 
4         42    9,707  25,141.00
# determine the range of density values
max_density = -1.0
min_density = -1.0
for index, row in df.iterrows():
    d = row['density/mi2']
    density = float(d.replace(',' , ''))
    if (max_density==-1.0) or (max_density<density):
        max_density = density
    if (min_density==-1.0) or (min_density>density):
        min_density = density
print('max',max_density)
print('min',min_density)
range_density = max_density - min_density
print(range_density)
('max', 1218.0)
('min', 1.0)
1217.0
# we pick a color for the state density out of color map
cmap = matplotlib.cm.get_cmap('Spectral')
# for each state get the color for it's density
for index, row in df.iterrows():
    state_name = row['State']
    d = row['density/mi2']
    density = float(d.replace(',' , ''))
    color = cmap((density - min_density)/range_density)
    seg = map.states[state_names.index(state_name)]
    poly = Polygon(seg, facecolor=color, edgecolor=color)
    ax.add_patch(poly)
plt.show()

We see a color-coded density map in the following figure. I am not sure why Minnesota and Wisconsin did not match up with the data (they show no color for the density in the map). The data file looks correct and does appear to map to the image points.