Definitions of economic migrants, war and climate change refugees, etc., are given. Their flow to Europe is studied as one-dimensional transport using the phenomenological theory of diffusion and by gravity model employed in urban geography. Diffusion of migrants is quantified by the diffusion coefficient expressed as [km2/day], appropriate also for the characterization of historical transfers of nations along large territories. Solutions of 2nd Fick’s law applied in semiconductor technology were adapted in the work. They show that in the future, due to the climate change followed by desertification of land and sea level rise, the immigration to Europe may obey diffusion from a constant (infinite) source and it may overflow the continent. Various desertification scenarios are summarized. Simplified gravity model was used to find which economic and demographic factors attract migrants. The distance as a standard variable in the gravity model does not play any role in the present migration movement. Migrants are attracted by high GDP and partly by populations of the country of destination. The gravity model studies provide also correlations between desertification of the land and other environmental variables, like soil erosion, deforestration, etc.