LIFTED HYPOTHESES AND MODELING OF SOME PARAMETERS

In view of the historical process of the urbanization of São Paulo, it was decided to raise some hypotheses that are directly linked to the concretization of the population growth of the city of São Paulo.

Nowadays, it is noted that large cities offer many employment opportunities, access to basic housing needs, access to health and education. These aspects concretize the pillars of the hypotheses raised to model this population growth.

With the increase of the urban population, the dynamics of the city change, and with that, it delves into issues of urban mobility, which is one of the great factors to plan urbanization. Thus, the diagram below demonstrates this relationship.

The rate of increase of a population is the sum of birth rates (n) and migration (g), minus the mortality rate (m):

The population increase at any given time is equal to the product of the population at that time by the rate of population increase. If the population at time t is represented by the function P (t), the population increase will also be equal to that derived from P.

By the Malthus Model, if the rate of population increase a is constant, the differential equation will be an equation of separable variables.

Where P0 is the population at t = 0. This model can be a good approximation in a certain interval, but it has the drawback that the population grows without limit.

The growing population of the city of São Paulo demanded the evolution of avenues and highways throughout the current metropolitan region, so a graphical relationship can be made with the growth of the city's population and the growth of automobiles in the city.

Raising the population data through sources such as the IBGE, it was possible to relate the growth through the number of cars in the city, since this means of transport is one of the most used, not only by the inhabitants of São Paulo, but in almost everything Brazilian territory. In 2015, there was a total of approximately 0.7 cars per person in São Paulo, that is, almost one car per inhabitant in the city of São Paulo.

However, the capital needed to acquire a vehicle, in addition to all bureaucracy, is not available to every citizen of São Paulo. For this reason, the analysis of population growth and urban planning turned to public transport. As the metro is one of the main and most democratic means of transport, observing the growth of the subway network will be the method used for the modeling analysis and the main focus of the urban planning study of one of the largest and most developed cities in the world, the city from Sao Paulo.