Mathematical modelling of the effects of urbanization and population growth on agricultural economics

Suhrit K. Dey, Chanchal Pramanik, Charlie Dey


Population growth often requires urbanization for both cultural and economic developments. However, there is a downside of this colourful scenario. Growing population requires more food consumption and urbanization, which requires more building construction, more roads, more shopping centers, more hospitals, more recreational centers, etc. To fulfill these demands, often lands for agriculture and ponds for fisheries, which should enhance food supply to meet demands for foods of vital significance, are being used to help urbanization. This could inevitably cause a disaster to a nation. The burning question is: how population, urbanization and food production can a1l be balanced. A modest attempt has been undertaken in this work to look for a mathematical solution. The authors have developed a mathematical model, which validates the possibility of an acute shortage of food production if the growth of population and rampant urbanization are not kept under control. Certain parameters related to the growth of population, urbanization and their impact on food production are taken into consideration. The model consists of three ordinary differential equations dealing with the interactions between these three interactive economies. It has been assumed that while population grows independent of urbanization and agricultural products, the rate of urbanization depends on the rate of growth of population, and food productions depend on both urbanization and population. To avoid any catastrophic shortage of food, an extra term has been added to the rate of the growth of food production. This could well represent food substitutes, urban gardening and/or importing food from other areas. By solving this system mathematically, it has been found that unless that extra source of food supply is kept in place, there could be a catastrophic shortage of food if both population and urbanization are uncontrolled. This simplistic model has established a strong qualitative agreement with real world scenario. The challenge is now to find the statistical estimates of the parameters in the model to fit the different agricultural economy of different parts of the world and predict the optimization of urbanization accordingly. Furthermore, availability of food does not necessarily make it affordable. People should be able to afford the price of their necessary food. An attempt has been made to estimate this price in terms of available agricultural production and the population who depend on it.


mathematical modeling; parameters of the growth of population; food interactive economies production

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"Intellectual Economics" ISSN online 1822-8038 / ISSN print 1822-8011