The aim of this paper is to study the relationship between the rate of demographic growth through epidemics and economic growth to verify the Malthus perspective on the one hand.And on the other hand, this work follows a methodology describing a comparative analysis between the effect of two types of population with and without pessimism of Malthus on the economic growth rate of GDP per capita over the last five years as cut data cross-section for some countries in North Africa and the Middle East.