How to spread a population data from a vector layer in a raster layer? [duplicate]

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I got a shapefiles for provinces in a African country. In each province there is the population data. I've got 3 TIFF (raster),

  • one for the agriculture,
  • one for the cities and
  • the last one for other (forest,lake, grassland etc...).
Knowing the population of each province, I've got to spread it according to the density. The density of cities are 100x the density of other and 5x the density of agriculture and the density of agriculture is 20x the density of other.

At the end I would like a population size for each pixel. How can I do it using the raster calculator or another tool in QGIS?



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